Boyhood, which took 12 years to make, won best film drama, with Richard Linklater named best director and Patricia Arquette best supporting actress.
Eddie Redmayne won best actor in a drama for his role as physicist Professor Stephen Hawking in The Theory of Everything.
Joanne Froggatt and Ruth Wilson also collected prizes.
The awards, which honor both film and TV, saw Joanne Froggatt win best supporting actress in a TV series for her role as the maid Anna Bates in Downton Abbey.
Ruth Wilson was named best actress in a TV drama for The Affair.
Collecting the best director award, Richard Linklater said: “I want to dedicate this to parents that are evolving everywhere and families that are just passing through this world and doing their best.
“Bottom line is we’re all flawed in this world. No one’s perfect.”
Eddie Redmayne beat competition from Benedict Cumberbatch, for The Imitation Game, and David Oyelowo, for Selma, to the best actor award.
On collecting his award, Eddie Redmayne revealed he cut short his honeymoon to attend the ceremony in Beverly Hills: “I promised her sunshine – it wasn’t so great today – but thanks for giving us a honeymoon we’ll remember.”
His co-star, Felicity Jones, missed out on the best drama actress award to Julianne Moore for her role as an academic with early onset Alzheimer’s in Still Alice.
Rosamund Pike and Keira Knightley were also nominated for their parts in Gone Girl and The Imitation Game respectively, but were both disappointed.
Birdman had led nominations going into the ceremony with seven nods. However, the film collected only two awards – one for Michael Keaton as best actor in a comedy or musical and one for best screenplay.
Whiplash star JK Simmons was the first winner of the night, collecting the prize for best supporting actor.
The Theory Of Everything also collected two of the four awards it was nominated for. Besides Eddie Redmayne’s prize, it was also award best original score by Johann Johannsson.
Wes Anderson’s The Grand Budapest Hotel won best comedy or musical film, with Amy Adams named best actress in a comedy or musical for her role in Big Eyes.
Despite being nominated for five awards, Alan Turing drama The Imitation Game came away empty-handed as did thriller Gone Girl, which had received four nominations.
Many of the actors spoke of their support for free speech following the Charlie Hebdo deadly attacks in Paris last week.
Some held “Je suis Charlie” signs on the red carpet, while others referred to it while on stage.
In the TV categories, Joanne Froggatt was surprised to win her award, beating the likes of Kathy Bates, Allison Janney, Michelle Monaghan and Uzo Aduba from Orange is the New Black.
Joanne Froggatt was rewarded for her portrayal of Anna Bates, who was raped and then accused of murdering her attacker in the drama.
“This is the most shocking moment of my life. After the storyline aired I received a lot of letters from survivors of rape – thank you to everyone who wrote – I heard you,” she said.
Maggie Gyllenhaal won best actress in a TV movie or mini-series for her role in The Honourable Woman.
Kevin Spacey picked up his first Golden Globe after eight nominations for his role in Netflix drama House of Cards.
Amazon comedy drama Transparent celebrated two award wins for the streaming service after it was named best TV comedy and its star, Jeffrey Tambor won best actor in a TV comedy for his role as a transgender woman.
Fargo also collected two prizes, winning best TV miniseries and best actor in a TV miniseries for Billy Bob Thornton.
The Affair was named best TV drama.
Other awards went to Gina Rodriguez for comedy series Jane the Virgin, and Matt Bomer for AIDS drama The Normal Heart.
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