The romantic musical about a struggling actress and a jazz pianist trying to make it in Hollywood took home Globes for Ryan Gosling as best actor, as well as for its screenplay, score and original song.
"La La Land" is also a favorite for the top prize - best comedy or musical film - that is given out at the end of the show and which would cement its front-runner status at the Oscars in February.
"This is for musical theatre nerds everywhere," said songwriter Justin Paul.
Composers Benj Pasek (L), Justin Hurwitz (C) and Justin Paul hold their awards for Best Original Song - Motion Picture for "City of Stars" from the film "La La Land" during the 74th Annual Golden Globe Awards in Beverly Hills, California, U.S., January 8, 2017. Photo: REUTERS
First-time Golden Globes host Jimmy Fallon welcomed the A-list audience and TV viewers to the ceremony, calling it "one of the few places left where America still honors the popular vote."
Ballots for the awards in film and television, Fallon, quipped were tabulated by accountants "Ernst and Young and (Russian President Vladimir) Putin."
Trump takes office on Jan. 20 after winning the U.S. presidential election but losing the popular vote to rival Hillary Clinton. U.S. intelligence agencies said in a report released last week that Putin ordered an effort to help Trump's electoral chances.
Viola Davis won as expected for playing a downtrodden wife in the African-American family drama "Fences," the movie version of the award-winning play by August Wilson.
"It's not everyday Hollywood thinks of translating a play to screen. It doesn't scream moneymaker, but it screams art, it screams heart," Davis said.
Netflix's British royal drama "The Crown" beat fantasy "Game of Thrones" and sci-fi series "Westworld" for best drama series, and brought a win for Claire Foy for playing Queen Elizabeth.
"I think the world could do with a few more women at the center of it," Foy said of the British monarch, who has been queen for more than 60 years.
Elsewhere, the Golden Globes lived up to their reputation for upsets, and black actors and stories were the biggest beneficiaries.
Hip hop show "Atlanta" won best TV comedy series, beating old favorites including "Veep" and "Transparent."
"This is incredible," said "Atlanta" creator and lead actor Donald Glover. "We didn't think anyone was gonna like this show so we really appreciate it."
Tracee Ellis Ross, a first-time Golden Globe nominee, was named best comedy actress for playing the mom in African-American family comedy "black-ish."
The Golden Globe for best limited TV series went to "The People v. O.J. Simpson; American Crime Story," whose behind the scenes dramatization of the 1995 double murder trial of the disgraced football player has won a slew of other awards. Sarah Paulson took home the award for playing prosecutor Marcia Clark.