The fact that "Brokeback Mountain" has found eager audiences across the country, including the conservative heartland, shows that Americans are willing to embrace stories of love in all forms, Lee said.
"It has proven you can never categorize a region or place or stereotype them," he said.
As expected, it was a triumphant night for films dealing with homosexuality and transsexuality. Along with the victories for "Brokeback Mountain," acting honors went to Felicity Huffman in a gender-bending role as a man preparing for sex-change surgery in "Transamerica" and Philip Seymour Hoffman as gay author Truman Capote in "Capote."
"I know as actors our job is usually to shed our skins, but I think as people our job is to become who we really are, and so I would like to salute the men and women who brave ostracism, alienation and a life lived on the margins to become who they really are," Huffman said.
Lee's "Brokeback Mountain," the story of two rugged Western family men (Heath Ledger and Jake Gyllenhaal) concealing their affair, has emerged as a front-runner for the Oscars -- which occasionally have handed out top acting prizes for performers in homosexual or gender-bending roles but have never given the best-picture Oscar to a gay-themed film.
Oscar nominations come out Jan. 31, with the awards presented March 5.
"Brokeback Mountain" also won for best screenplay and song, "A Love That Will Never Grow Old."
Phoenix and Witherspoon won for best actor and actress in a movie musical or comedy for the biopic that follows country legend Cash's career and his long courtship with the love of his life, June Carter.
The Globe audience clapped along to Cash's song "I Walk the Line" as Phoenix took the stage.
"Who would ever have thought that I would win in the comedy or musical category?" said Phoenix, poking fun at his image for dark, brooding roles. "Not expected."
Phoenix, who did his own singing in the film, thanked "John and June for sharing their life with all of us."
"This film is really important to me," said Witherspoon, who offers a spirited performance and fine singing as Carter. "It's about where I grew up, it's about the music I grew up listening to, so it's very meaningful."
George Clooney, who was among the directing nominees for "Good Night, and Good Luck," won the supporting-actor Globe for the oil-industry thriller "Syriana" and Rachel Weisz earned the supporting-actress prize for the murder thriller "The Constant Gardener."
The Palestinian film "Paradise Now," a dark tale of two Arab friends tapped to carry out a suicide bombing in Israel, won the prize for foreign-language film.
Television winners included Geena Davis for best drama series actress as the U.S. president in "Commander in Chief," Hugh Laurie for drama series actor as a cranky, pill-popping doctor in "House," Steve Carell for best comedy series actor as an incompetent boss in "The Office," Jonathan Rhys Meyers for miniseries or movie actor as Elvis Presley in "Elvis" and S. Epatha Merkerson for miniseries or movie actress as a boarding house proprietor who takes in an outcast teen in "Lackawanna Blues."
"This is really wonderful for a fledgling little show like ours," said Davis, who added that a little girl coming into the Globes stopped her to say, "Because of you I want to be president some day.
"Well, that didn't actually happen," Davis joked. "But it could have."
Mary-Louise Parker of "Weeds" beat out the four lead actresses of "Desperate Housewives" for best actress in a comedy series.
"I know everyone thinks they have the best cast but I ... just get to go work with such great actors who are so talented ... who are so wonderful and kind and good and wonderful and sexy and great and I just want to make out with all of you," Parker said.
But "Desperate Housewives" did win for best musical or comedy series.
The Globes are awarded by the relatively small Hollywood Foreign Press Association, which has about 80 members, compared with the 5,800 film professionals eligible to vote for the Oscars.
Still, the Globes have an excellent track record at predicting the Oscars. Globe winners catch momentum that can boost their chances come Oscar night.
The Associated Press contributed to this report.