Cillian Murphy and Robert Downey Jr were recognised for their acting in it while Christopher Nolan picked up best director for the film.
Corporate drama Succession had most wins in the TV categories after its praised fourth and final season.
Barbie scooped the inaugural cinematic and box office achievement award, taking in a market-leading ÂŁ1.13billion worldwide. There were two wins each for Anatomy of a Fall, The Holdovers and Poor Things.
Sole honour for Martin Scorseseâs epic Killers of the Flower Moon was Lily Gladstone being named best drama actress â making her the first indigenous person to win that award, a moment she called âhistoricâ.
Oppenheimer star Murphy paid tribute to Nolanâs ârigour, focus and dedicationâ in making the film, which grossed ÂŁ750million at the box office and won best drama.
The biopic also grabbed best score plus best supporting actor, for Downey Jrâs portrayal of US government official Lewis Strauss.
Murphy, who played J Robert Oppenheimer â the theoretical physicist known as âthe father of the A-bombâ â said: âI knew the first time I walked on Christopher Nolanâs set that it was different.â
He quipped: âI could tell by the level of rigour, focus, dedication and the complete lack of seating options for actors that I was in the hands of a visionary director.â
Murphy also joked about the number of Irish stars in awards season â nominees in his category included Saltburnâs Barry Keoghan and All of Us Strangers actor Andrew Scott.
He added at the star-studded ceremony in the Beverly Hilton, Beverly Hills: âTo all my fellow nominees, whether youâre Irish or not, youâre all legends, I salute you.â
The UK had modest success, with six wins in 27 categories: three for individual performers and three for co-productions with other countries.
Matthew Macfadyen won best male supporting actor in a TV series for Succession; Ricky Gervais collected best performance in TV stand-up comedy for one-off Armageddon, plus Nolanâs director gong.
It is his first major directing award despite a successful movie career including Oscar, Bafta and Golden Globe nominations for films such as Memento, Inception and Dunkirk.
Nolanâs Oppenheimer was also one of Britainâs three joint wins.
The US-UK co-production was named best motion picture drama; Poor Things, a dark comic fantasy produced by Ireland, the UK and the US, was best motion picture musical or comedy while Barbie was also a US-UK co-production.
The Golden Globes has long been dominated by the US.
The UKâs tally of six wins this year is the highest since 10 in 2020 and 2021 and is an improvement on last year â when the total was just two.