Its stars Amy Adams and Jennifer Lawrence also picked up best actress and supporting actress prizes for their roles in the 1970s-set crime movie.
Steve McQueen’s 12 Years a Slave picked up the top honour of the night, winning best film drama.
However, it was the only award 12 Years a Slave picked up, after going into the evening with seven nominations.
Both Steve McQueen and stars Chiwetel Ejiofor, Michael Fassbender and Lupita Nyong’o had received nods but came away empty-handed.
Collecting the award, Steve McQueen said he was “a little bit in shock” and thanked his wife for finding the book by Solomon Northup, on which the film was based.
The other film awards were spread around a number of movies.
Matthew McConaughey was named best actor in a drama for his role as AIDS patient Ron Woodroof in Dallas Buyers Club.
The actor said the award was “unexpected, but graciously accepted”.
His co-star Jared Leto also won the best supporting actor prize for his depiction of a transgender woman.
Cate Blanchett collected the best actress in a drama award for her part as a disgraced socialite in Woody Allen’s Blue Jasmine, while Leonardo DiCaprio won best actor in a comedy or musical for The Wolf of Wall Street.
Leonardo DiCaprio, who won his second Golden Globe after nine nominations, thanked director Martin Scorsese for his mentorship and for “allowing me to stalk you to make this movie”.
Alfonso Cuaron was named best director for Gravity – the only award the space movie picked up on the night – beating Steve McQueen, Paul Greengrass for Captain Phillips, Alexander Payne for Nebraska and David O. Russell for American Hustle.
The screenplay award went to Spike Jonze for his comedy romance Her. Italian film The Great Beauty won the title of best foreign language film and Disney’s Frozen took home the best animated feature award.
Robert Redford’s film All is Lost won the best original score prize, while Irish band U2 won best original song for Ordinary Love, as featured in Mandela: Long Walk to Freedom.
Coldplay and Taylor Swift had also been in the running for their songs from Hunger Games: Catching Fire and Paul Potts film One Chance respectively.
As the first major ceremony of the awards season, the winners are a likely indication of Oscar recognition when the nominations are announced later this week.
The TV categories featured a number of double award winners.
Liberace biopic Behind the Candelabra was named best TV movie/mini-series, with Michael Douglas picking up the best actor in a TV movie, series or mini-series, beating his co-star, Matt Damon.
Although the film was released in cinemas around the world, it was only shown on cable channel HBO in the US.
Breaking Bad also came away with two awards including best drama series and best actor in a drama for its star Bryan Cranston.
It was the first Golden Globe for Bryan Cranston, having been nominated for the same award every year since 2011. He was also nominated in 2003 for his role in comedy Malcolm in the Middle.
He called the award “a lovely way to say goodbye” after the series ended after five years in September.
Police caper Brooklyn Nine-Nine also collected two prizes including best comedy or musical TV series and best actor in a comedy for Andy Samberg.
Amy Poehler won best actress in a TV comedy or musical for her role in Parks and Recreation, while Robin Wright was named best actress in a drama series.
Elisabeth Moss won best actress in a TV movie or mini-series for Top of the Lake and veteran actor Jon Voight collected best supporting actor in a TV movie, series or mini-series for Ray Donovan.
Jacqueline Bisset won best supporting actress in a TV series, mini-series or TV movie – for her part in drama Dancing on the Edge.
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