SAN PEDRO SULA, Honduras—Luis Javier Tejada is an example of why, in many ways, there has never been a better time to be gay in Honduras.

Last year, the graphic artist rejoiced as two openly gay candidates ran for the Honduran National Congress, which had just passed a broad measure against hate speech based on “sexual orientation or gender identity.” This spring he was looking forward to drawing a salary from a Dutch group supporting his work with HIV-positive Hondurans.

But cultural change comes slowly. Neither gay candidate came close to winning—and one fled Honduras after reporting that a mob ransacked her offices and savagely beat her. Mr. Tejada’s partner also fled. Both sought asylum in New York, where Mr. Tejada, 33 years old, hopes he will soon do the same.

For that, he will rely on something most aspiring immigrants here can’t: membership in a class the U.S. State Department recognizes as under attack. “Social discrimination against LGBT persons was widespread” in Honduras, reads the department’s 2013 international human-rights report, using an acronym for lesbian, gay, bisexual and transgender people. The report notes that “NGOs reported 24 violent deaths of LGBT individuals” through last September.

Luis Javier Tejada, 33, a graphic artist and HIV activist, said he is hoping to leave San Pedro Sula to seek asylum in the U.S. He said gangs threatened him. Alicia Vera for The Wall Street Journal

Such official assessments have fueled a surge of successful asylum petitions from gays and lesbians in the Americas. Arguing that they suffer persecution because of their sexual orientation, hundreds if not thousands have managed to find safe haven, and a potential path to U.S. citizenship, in recent years. Fellow Latin Americans lodging asylum claims based on generalized violence, meanwhile, are routinely denied.

Many Hondurans wind up on the South Bronx couch of Fredy Triminio, a Honduran gay-rights activist who says he has guided nearly 50 countrymen into the process since 2009, when the 41-year-old gained asylum himself. “Honduras is known now as a place where it is dangerous to be gay,” he says.

How it got that way says a lot about sweeping changes in U.S. asylum policy, and the power of a dedicated lobby. During the Cold-War years, most asylum-seekers claimed they were persecuted by their governments for political reasons. Today, applicants are more likely to say they are threatened by religious persecution or myriad social ills, from female genital mutilation to spousal abuse.

Among the biggest new beneficiaries, based on a reading of federal data and interviews with immigration experts, are sexual minorities. Last year, just one New York-based advocacy group, Immigration Equality, helped put 279 LGBT foreigners into the asylum process, a 250% increase from 2009. Altogether, the group has helped 1,130 people seek asylum in the past decade, with 421 cases still pending. Their success rate for closed cases: 98%, roughly quadruple the batting average of the typical asylum-seeker.

The jump in gay asylum cases tracks a growing willingness by Americans to embrace alternative lifestyles as well as a determination by U.S. foreign-policy officials to protect sexual orientation as a basic human right. In recent months, American leaders have denounced a new law in Russia criminalizing “recruitment” by gays, as well as practices in places such as Uganda and Nigeria that punish homosexuals with severe sentences, even death.

A close analysis of asylum trends, though, suggests that most gay asylum seekers don’t come from these high-profile countries, but rather from the Americas. Data compiled by Homeland Security’s U.S. Citizenship and Immigration Services unit don’t break out asylum claims for gays and lesbians, who typically apply under a catchall category called “member of a particular social group.” According to data released to The Wall Street Journal under the Freedom of Information Act, the largest source countries over the past decade were Mexico, Guatemala, Colombia and Haiti, with Russia coming in fifth place. Nine of the top 25 were from the Americas.

The rise in gay asylum cases comes at a time of soaring bloodshed in Latin America. Newly released United Nations data show that Latin America is the world’s most violent region, accounting for nearly one in three global homicides. The worst homicide rate by far belongs to Honduras, where 7,172 people were murdered in 2012, or 90.4 out of 100,000. The U.S. rate, by contrast, is 4.7.

Some human-rights advocates in the region believe the U.S. should modify its asylum policies to make a place for average citizens caught in the crossfire. Juan Wilfredo Castellanos, northern Honduras’ official human rights commissioner, says a lot of his country’s violence should be classified as persecution under international asylum norms because much of it stems from the government’s inability to protect its citizens.

“The authorities here don’t have the resources to investigate crime, let alone stop it,” the lawyer says wearily, adding that as the murder rate climbs, so has the tide of would-be refugees who want their “denunciations” of death threats they have received archived by his staff, to present as evidence in a future asylum application once they leave Honduras.

But merely stating you have been threatened doesn’t work for everyone. Juan Manuel Jimenez, a 31-year-old father from the coastal city of La Ceiba, spent about $2,000 last summer to sneak into the U.S. In Texas, U.S. Border Patrol agents arrested his crossing party. He immediately tried to open an asylum case, saying he was persecuted by “narco-traffickers, who threatened me with death.” He failed.

“The judge said I didn’t qualify for asylum,” said Mr. Jimenez. He spent four months in detention before agreeing to drop his appeal and board one of Homeland Security’s daily repatriation flights to San Pedro Sula—one of 37,049 Hondurans deported in 2013.

Carlos Flores, 27, Mr. Tejada’s partner, fled San Pedro Sula for New York last year and was granted asylum after about four months. He said he had been tortured by police in Honduras. Joel Millman/The Wall Street Journal

The outcome was quite different for Carlos Flores, who fled San Pedro Sula for New York last year. The 27-year-old bookkeeper kept a low profile in this dangerous city, but was involved with LGBT civil-rights activists through his partner, Mr. Tejada, the HIV activist here.

Mr. Flores says three police officers detained him in January 2013, along with a transgender activist named Beyoncé who works with street walkers. The two were tortured to provide information on a transgender activist wanted by police, Mr. Flores says. He adds that the officers promised to return for more punishment if they didn’t find their suspect.

“They said they’d kill me,” said Mr. Flores, who fled Honduras a few days later. After leaving San Pedro Sula, Mr. Flores ended up in the South Bronx, sofa surfing among an enclave of gay Hondurans in the apartment of Fredy Triminio.

“It was easier for everyone after my case,” said Mr. Triminio, who explains that his archive of hate crimes committed against LGBT Hondurans often finds its way into the evidence packets asylum seekers prepare. The claims are almost always successful, he says.

Like many gay refugees, Mr. Flores turned to Immigration Equality. He made his asylum application early last December represented by a pro bono attorney, David Castleman, a graduate of the University of Pennsylvania Law School now working for the firm Sullivan & Cromwell LLP.

Mr. Flores’ asylum quest took less than four months. He received his grant of asylum, which gives him permanent residence status, or a green card, on March 6.

Fernanda Vallejo, a transgender Honduran fleeing violence against LGBT people in her country, is seeking asylum in the United States. Watch a video about her journey. Photo: Natalie Keyssar for The Wall Street Journal

Such fast turnarounds were a long time in coming. Once barred as “deviants” from emigrating to the U.S. under any circumstances, gays saw their stigma partially lifted for asylum purposes in 1990. They gained recognition as members of a particular social group after the Board of Immigration Appeals ruled in favor of a Cuban refugee who had been jailed and tortured for his sexual orientation.

Michael Petrelis, an organizer for the group Gays Without Borders, says he began lobbying the U.S. State Department to monitor what he and others called “atrocities” against gays world-wide starting in 1991, as an Act Up militant in Washington. “We tried all approaches,” says the 55-year-old activist, who lives now in San Francisco. “Winning asylum for those who got here. Fighting to document attacks. Using the State Department’s annual human rights reports so our folks could gain asylum.”

Accounts of specific hate crimes against homosexuals, or of crimes targeted at LGBT leaders, began to appear in the late 1990s in the annual reports for a handful of countries. By the middle of the next decade documentation was becoming systematic, with the condition of sexual minorities addressed in most places around the world.

The reports have turned out to be a key element in successful asylum cases. “Often the only objective evidence is the U.S. State Department’s report,” says William Zimmer, who presided as an immigration court judge in Houston until 2012.

Since many asylum precedents are set by federal courts, no one presidential administration can move the needle significantly. But activists credit the Obama White House with nudging the issue higher on the agenda.

Transgender prostitutes worked on the street in San Pedro Sula. A U.S. State Department report notes high levels of discrimination and violence against gay people in Honduras. Alicia Vera for The Wall Street Journal

LGBT migrants have become so commonplace among those apprehended along the border that Homeland Security has opened two detention centers for them since 2011—one in Pearsall, Texas, the other in Santa Ana, California. That same year the administration also issued a memorandum stating that community ties—including for the first time, same-sex relationships—could help a detained migrant win release pending a court appearance.

The administration has also issued a series of orders and memos spelling out how LGBT asylum cases should be handled.

A 65-page publication, “Guidance For Adjudicating Lesbian, Gay, Bisexual, Transgender, and Intersex (LGBTI) Refugee and Asylum Claims” prepared for USCIS asylum officers in December 2011, notes that “the fact that LGBTI organizations are permitted to hold a parade once a year…does not mean LGBTI people are free from ongoing violence and harm in that country.” The training material, which the Immigration Equality activist group says it helped prepare, explains that the guidelines for gay asylum applicants are the same as for any other asylum-seeker.

In fact, though, the instructions appear to carve out some exceptions. For instance, asylum policy states that individuals generally have no more than a year to lodge a petition once they arrive in the U.S. The guide notes that LGBTI individuals who come to the U.S. for work or school, and weren’t fleeing violence, might “come out” after arriving. Their asylum claim would be based on a fear of persecution if they returned home.

Immigration officials and advocates said they weren’t aware of any cases involving an applicant faking being gay to gain asylum. As with any asylum-related fraud, the potential penalties are severe, including being banned from the U.S. for life. “Asylum officers are trained extensively in interviewing techniques, evaluating evidence, researching country of origin information, and analyzing credibility based on objective criteria,” a USCIS spokesman says.

The country reporting by the State Department became a higher priority under the Obama administration. “As posts affirmatively raise concerns about the rights of women, religious minorities, and other vulnerable persons, posts also should raise any concerns about the human rights of LGBT persons in meetings with host government officials and other civic and business leaders,” Secretary Hillary Clinton wrote in 2010 in an instruction telegram cable to all diplomatic and consular posts.

The secretary emphasized: “posts are requested to proactively identify and engage LGBT civil society groups, and to assess and respond to threats to the human rights of LGBT persons.”

That is occurring in a big way in Honduras, even though the official legal climate here, as in much of Latin America, is relatively favorable to sexual minorities.

Last year, Honduras’ National Congress amended the penal code to sanction anyone “who publicly or through the media incites discrimination, hate, repression, or violence against a person or group for reasons of their sex, gender, age, sexual orientation,” a development U.S. diplomats praised.

Charles Blaha, a State Department official monitoring human rights progress in Latin America, suggests that good laws alone don’t mean some people in the LGBT community don’t deserve asylum consideration. “The fact is, in many of these countries, even though the government is doing good things and trying hard, these are entrenched societal attitudes and they play themselves out sometimes in very ugly, violent ways,” he says.

The U.S. embassy in Tegucigalpa wields big influence. The U.S. dispenses millions in foreign aid to fund AIDS clinics. The U.S. also started funding, in 2011, a special victims unit under the Public Ministry for investigating hate crimes against gays and others.

A common route from San Pedro Sula, Honduras, to the U.S. border, in part on the dangerous freight train known as ‘La Bestia.’

The unit, based in San Pedro Sula, hasn’t stopped much crime, says federal prosecutor Norma Zobeida Narvaez, who runs the unit. But the effort has benefited asylum seekers, essentially by documenting crime against sexual minorities—and demonstrating how infrequently such crime meets punishment.

Over the past three years, State Department reporting indicates nearly 100 LGBT individuals have been murdered in Honduras.

However, human-rights workers and diplomats acknowledge that, given the general level of violence in San Pedro Sula, it is often hard to know if the murders had anything to do with the victim’s sexual orientation. The area has become a key transit point for narcotics leaving South American and headed north, and there is a high degree of police corruption. On most days, and especially nights, the city can resemble a shooting gallery.

Ms. Narvaez pulled the file of one person murdered in 2012—a transgender street walker shot to death by a customer who ran home to get his gun after he suspected his pocket had been picked during the encounter.

“But the one he shot was not the one who serviced him. He made a mistake,” said the prosecutor. “So can we really classify this as a hate crime?”

Carlos Fernando Vallejo, a transgender prostitute-turned-activist from San Pedro Sula known as Fernanda, cited a similarly ambiguous event in a complaint to the local human-rights commission. In January 2013, Ms. Vallejo said a prostitute with the street name Nahomi came at her with a knife. “I defended myself and Nahomi fell to the street,” Ms. Vallejo testified in a statement. “Later Nahomi sent some gang guys to threaten me.” She later claimed she was insulted and beaten by gang members who told her they wanted to “get rid of maricones,” a vulgar word for homosexuals. Ms. Vallejo entered the U.S. illegally through Mexico and is now seeking asylum.

René Perdomo, a Honduran gay activist who arrived in New York for a United Nations conference in April 2011 and decided to bid for asylum after overstaying his tourist visa, received the benefit of the doubt.

“It was a really easy process,” recalls the 29-year-old, whose evidence packet included affidavits from three Hondurans vouching for his character and citing his work with a transgender collective.

Mr. Perdomo also presented a résumé, and a stack of newspaper clippings chronicling attacks on gays in his homeland. He said his own life was endangered, and that gangs and police had threatened him, but wasn’t required to show any proof.

“I got my asylum on 16 April [2013]. The whole thing took eight months,” he says. He lives today in Roseburg, Ore., where he works at a Mexican restaurant. He says he plans to apply for U.S. citizenship as soon as he is eligible, in about four years.