"This award is for every woman who felt like there wasn't a space for her," said the 26-year-old writer-actor, who was practically unknown until last year, with the premiere of her off-kilter comedy about the travails of young women in New York.
Dunham won lead actress, and "Girls" took the TV comedy or musical series category. The show was nominated for five Emmys in September but got just one, for casting. As it happened, the Globes' honors came on the night the show's second season debuted on HBO.
For the TV industry, Dunham's triumph was the only surprise on an awards list otherwise marked by the familiar and the predictable. But there was an interesting footnote: This year marked the first time that no show on one of the four major broadcast networks received a Globe — including NBC, which aired the ceremony live. The show was co-hosted by Tina Fey of "30 Rock" and Amy Poehler of "Parks and Recreation," both of whom were nominated but did not win.
The drama award went to Showtime's counter-terrorism thriller "Homeland," which took the category last year as well.
Claire Danes, who plays troubled CIA officer Carrie Mathison on "Homeland," repeated in the lead actress category, while Damian Lewis, who lost to Kelsey Grammer last year, this time won for his work as an ex-Marine sergeant and ex-POW.
Another big honoree was HBO's "Game Change," which dramatized Sarah Palin's surprise ascension to the GOP ticket in the 2008 presidential campaign.
Julianne Moore won for playing the former vice presidential nominee, while Ed Harris took supporting actor as Sen. John McCain, who tapped Palin as his running mate. "Game Change," which depicted Palin as a determined, self-made politician who was hopelessly out of her depth in a national campaign, also won for TV movie-miniseries.
Palin, who last year attacked the movie for being based on a "false narrative," got a swipe from "Game Change" director Jay Roach as he hailed Moore's win. "Now, with you and Tina Fey, we have three of the most incredible impersonations of Sarah Palin," he said onstage, "counting Sarah Palin." In her acceptance speech, Moore thanked Fey and even Katie Couric — with whom Palin tangled in an infamous interview — but not Palin herself.
British actress Maggie Smith, denied a Globe last year for her work on PBS' "Downton Abbey," won in the supporting actress category this time. And Kevin Costner won as the hard-bitten patriarch in one of cable's biggest hits last year, History's miniseries "Hatfields & McCoys."
But the night belonged to Dunham, who was seen hobbling in high heels she admitted she wasn't used to wearing. "If I was as brave and reckless as people thought I was, then I would've worn flats to a show like this," she said backstage.
PHOTOS: 2013 Globes red carpet
LIST: Complete list of nominees
PHOTOS: Quotes from the stars