The night's top prize - best drama film - went to Nomadland, which stars Frances McDormand as a homeless woman travelling through the American West.
Chloé Zhao was named best director - becoming only the second female winner of the category in Globes history, after Barbra Streisand in 1983.
"Thank you everyone who made it possible to do what I love," Zhao said.
"I fell in love with making movies and telling stories because it gave us a chance to laugh and cry together, to learn from each other, and to have more compassion for each other."
Borat Subsequent Moviefilm, the sequel to 2006's hugely successful Borat, was named best musical or comedy film.
"Thank you to the all-white Hollywood Foreign Press," said Sacha Baron Cohen as he accepted the prize, referring to the recent revelation that the organisation behind the Globes currently has no black members.
Cohen poked further fun at the awards body as he was named best actor in a comedy or musical for the same film.
"Wait, Donald Trump is contesting the result. He's claiming that a lot of dead people voted, which is a very rude thing to say about the HFPA," he joked.
Borat and Nomadland were among several films to pick up two awards each. Of the night's 14 acting winners, half were British, including Cohen; Rosamund Pike, who was named best actress in a musical or comedy film for I Care A Lot; and Daniel Kaluuya, who won best supporting actor for Judas and the Black Messiah.
Kaluuya plays US activist Fred Hampton, the chairman of the Black Panther Party, who was assassinated in 1969 at the age of 21.
"I hope generations after this can see how brilliantly he fought, he spoke, and he loved," Kaluuya said as he accepted his prize.
"He taught me about myself, made me grow as a man, and I appreciate that with all my heart."