The British pop star and co-writer Paul Epworth won for best song for their theme tune to the 0007 adventure Skyfall.
Affleck's Iran hostage thriller Argo was a surprise best drama winner, beating Steven Spielberg's Civil War epic Lincoln, which had emerged as an awards-season favourite. Affleck also claimed the directing prize, despite not even being nominated for an Oscar.
In a breathless, rapid-fire speech, he gushed over the names of the other nominees Steven Spielberg, Ang Lee, Kathryn Bigelow and Quentin Tarantino. "Look, I don't care what the award is. When they put your name next to the names she (presenter Halle Berry) just read off, it's an extraordinary thing in your life," Affleck said.
Les Miserables was named best musical or comedy, while Hugh Jackman and Anne Hathaway claimed acting prizes. Hugh was named best musical or comedy actor, while Anne picked up the gong for best supporting actress.
"Thank you for this lovely blunt object that I will forevermore use as a weapon against self-doubt," Anne said.
Lincoln came into the ceremony leading with seven nominations but lost all but one, for Daniel Day-Lewis as best actor in the title role. "If I had this on a timeshare basis with my wonderful gifted colleagues, I might just hope to keep it for one day of the year, and I'd be happy with that," he said.
Other acting prizes went to Jennifer Lawrence as best musical or comedy actress for the oddball romance Silver Linings Playbook and Austrian Christoph Waltz as supporting actor for his role in Quentin Tarantino's slave-revenge tale Django Unchained. Tarantino won the screenplay prize.
The Scottish tale Brave won for best animated film. Austrian director Michael Haneke's Amour won the Globe for foreign-language film, while the prize for musical score went to Mychael Danna for the lost-at-sea tale Life Of Pi.