Cate Blanchett won best actress for Tar, becoming Australia's sole trophy winner at the 80th annual awards show on its return to TV after a diversity and ethics scandal.
The actress was unable to accept the award in person because she is filming in the UK.
The Fabelmans, a coming-of-age story based on Spielberg's teen years, was named best movie drama at the star-studded ceremony.
Banshees of Inisherin, the story of feuding friends on an Irish island, won best movie musical or comedy.
The awards are likely to give both movies a boost on the road to the Academy Awards in March.
Blanchett's win on Tuesday followed losses for fellow Aussies Hugh Jackman, Margot Robbie, Baz Luhrmann and Elizabeth Debicki.
Luhrmann was up for best director for Elvis but lost to Steven Spielberg for his coming-of-age movie The Fabelmans, which along with Elvis was vying with sci-fi blockbuster Avatar: The Way of Water for the evening's top honour.
However, Elvis claimed a best actor win for star Austin Butler.
"I'm in this room with all my heroes," Butler said while accepting the award.
"I can't believe I'm here. Brad (Pitt), I love you. Quentin (Tarantino), I printed out the script of Pulp Fiction when I was 12 years old."
The flashy Elvis biopic and sci-fi blockbuster Avatar: The Way of Water were vying for the top honour of best drama film against The Fabelmans and Tar.
Top Gun: Maverick also was in the mix, though the military action film's chances were likely hurt by star Tom Cruise returning his Globe statues in protest in 2021, awards experts said.
Veteran actor Michelle Yeoh also took a top movie award for Everything Everywhere All at Once, beating Robbie for her role in Babylon.
"Hollywood was a dream come true until I came here," the actor, of Malaysian descent, said, noting that she was called a "minority" and asked if she could speak English early in her career.
Colin Farrell, who won lead actor in a movie musical or comedy for his work in the dark Irish comedy Banshees of Inisherin, thanked his fellow cast members, including Jenny the Donkey.
In TV categories, Julia Garner won best supporting actress in a TV series for Ozark, beating Debicki for her portrayal of Princess Diana in the fifth season of The Crown.
Abbott Elementary creator and star Quinta Brunson was honoured as best actress in a TV musical or comedy.
Celebrities and broadcaster NBC abandoned the 2022 Globes because of ethical lapses at the Hollywood Foreign Press Association (HFPA), the group that hands out the awards.
A larger, more diverse membership and other changes by the HFPA persuaded many of the biggest movie and TV stars to support this year's ceremony, which provides publicity for winners and nominees and often boosts their chances at the Oscars.
The show unfolded largely as it had in years past, except for a biting monologue from comedian and host Jerrod Carmichael who opened the show joking, "I'm here because I'm black".
"One day you're making mint tea at home. The next day you're invited to be the Black face of an embattled white organisation," he said at the ceremony, which was broadcast live on the NBC network and streamed on Peacock.
Roughly 200 journalists and others from the international film industry voted on this year's Globes.
Among those voters, almost 52 per cent are racially and ethnically diverse, including 10 per cent who are Black, according to the HFPA.
