Cillian Murphy and Robert Downey Jr. were honored for their acting performances, and Christopher Nolan won the award for best director of the film.
Murphy played Robert Oppenheimer, known as the father of the atomic bomb, in the film, which earned nearly $1 billion at the box office.
The actor credited Nolan's "rigor, focus and dedication."
"Ever since I first walked onto Christopher Nolan's set, I knew this was something different," he said in his acceptance speech.
"By the rigor, focus, dedication and complete lack of space for the actors, I knew I was in the hands of a visionary director," he added.
Murphy also joked about the number of Irish nominees at this year's awards season - including Andrew Scott and Barry Keegan.
"To all my fellow nominees, whether you're Irish or not, you're all legends, congratulations," he said.
The biopic also won awards for best score and best supporting actor for Downey Jr., who played US government official Lewis Strauss.
Downey Jr. acknowledged the film's unlikely box-office success in his acceptance speech, joking, "A big story about the ethical dilemma of nuclear weapons makes $1 billion?"
The actor continued: "Since the summer, dozens of people have approached me saying that I was unrecognizably subtle as Lewis Strauss. To my fellow nominees, let's not pretend that's a compliment."
He also mentioned the changes made to the composition of the Golden Globes after a corruption scandal and lack of diversity. "Thank you for changing your game," he said.
Emma Stone was named best actress in a musical or comedy for her performance in "Poor Things," in which she plays the young Bella Baxter who travels the world to discover herself and awaken sexually.
"Bella falls in love with life itself rather than a person, she accepts the good and the bad equally," Stone said in her acceptance speech.
"And it really made me look at life in a different way and that everything in it matters. It stayed with me deeply, so that means a lot to me."
Stone thanked director Yorgos Lanthimos, saying she would be "forever grateful we met," and screenwriter Tony McNamara. "I love delivering that dialogue and I love horrifying you with my Australian accent," she joked.
"Barbie" still hasn't won as many awards as expected, but Billie Eilish won Best Original Song for What Was I Made For? - one of three songs that were nominated from the film's soundtrack.
"It was exactly a year ago when I was shown the film, and I was very unhappy and depressed at the time, and writing this song kind of saved me," Eilish said.
Da'Vine Joy Randolph won Best Supporting Actress for her role in "The Holdovers" as a woman who experiences overwhelming grief after the death of her son.
"Mary, you changed my life, you made me feel seen in so many different ways," she said, referring to the character she plays. "And I hope I've helped all of you find your inner Mary, because we all have a piece of her."
Court drama "Anatomy of a Fall" was awarded for best screenplay. Its director Justin Trier recalled the process of writing the film with his partner Arthur Harari.
"We were in a pandemic," she recalls, "and my life partner and I spent our days together writing the script for the movie, stuck in our apartment — and strangely, no one died."
Among the first winners in the television categories are Steven Yeon and Ali Wong - who were honored for their performances in "Beef"./BGNES
