The two openly gay athletes appeared along with human rights activists at the U.N. events, which focused attention on the upcoming Winter Olympics in Sochi, Russia.
Russia passed a law this summer banning homosexual "propaganda." The law has drawn international condemnation and sparked some calls for a boycott, though no nations have threatened to pull their athletes.
Navratilova, who lost lucrative endorsements when she came out back in 1981, said she doesn't support any boycotts. But she said the IOC is "putting its head in the sand" and criticized FIFA, the world soccer body, for awarding the 2022 World Cup to Qatar.
"Nobody's talking about Qatar and the World Cup. You can get a jail term there," she said of consensual gay sex in the small Persian Gulf nation.
Collins paid his respects to Navratilova, thanking her for coming out back when such a move ended up costing her millions in lost endorsement opportunities.
"I'm sitting next to one of my idols," he said.
North America's major pro sports leagues are still awaiting an openly gay athlete. Collins, 35, was prepared to become that pathbreaker when he came out as gay in April, after the NBA regular season had ended and he became a free agent. The aging reserve player has not been signed by another team, though he says he stays in shape and still hopes to return to the NBA.
In a related event, U.S. U.N. ambassador Samantha Power called the Russian law "as outrageous as it is dangerous."
Power, who was meeting with dozens of gay activists from around the world, said 78 countries still have laws that criminalize consensual sex between adults.
"To deny gays and lesbians the right to live freely ... is in fact barbarian," Power said.
She added that this year was the first time the U.N. held a ministerial meeting on LGBT issues, with Secretary of State John Kerry attending. "That's progress," she said.
Russian journalist and gay right activist Masha Gessen then read part of the Russian law on gay "propaganda" and said, "It actually enshrines second-class citizenship and makes it a crime to talk about equality."
Zambian activist Juliet Mphande listened to Gessen's comments and said, "I imagine Russia to be an African country right now." She said at least six people from her country's gay community had been arrested this year.