Windsor died Tuesday in New York at 88. The cause of her death wasn't given, but she had struggled with heart issues.
Clinton described Windsor, who had a master's degree in mathematics and worked for IBM, as "a path breaker first in science and computers and then in social history and politics and culture."
"She helped change hearts and minds, including mine, and we are forever grateful to her for that," said Clinton, the 2016 Democratic presidential nominee, who first announced her public support for same-sex marriage in 2013.
Clinton's remarks came as hundreds of people gathered for Windsor's funeral at Temple Emanu-El in Manhattan.
Windsor was 81 when she brought a lawsuit that proved to be a turning point for gay rights. The impetus was the 2009 death of her spouse, Thea Spyer, a psychologist.
The women had married legally in Canada in 2007 after spending more than 40 years together, but under the U.S.
The justices ruled 5-4 in June 2013 that a provision in the law barring the U.S. government from recognizing same-sex unions was unconstitutional.
The opinion didn't legalize same-sex marriage, but it ultimately became the basis for a wave of federal court rulings that struck down state marriage bans and led to a 2015 Supreme Court ruling giving same-sex couples the right to marry from coast to coast.
"She refused to give up on the promise of America. There wasn't a cynical, defeatist bone in her body," Clinton said Friday. "That's especially important for us to remember now."