Steve McQueen's hit film starring Chiwetel Ejiofor took home best movie drama at the glitzy ceremony in Beverley Hills, California, and will now be widely tipped for Oscar success.
It saw off competition from Captain Phillips, Gravity, Philomena and Rush to become a success story for Britain.
The win provided a well-need boost for Britain, after a number of leading actors and actresses missed out on wins despite nominations.
Idris Elba and Chiwetel Ejiofor had been tipped for the most success, going head-to-head with each other for two gongs before both losing out.
Elba, who rose to fame in US drama The Wire, was nominated for best actor in a motion picture for his performance as Nelson Mandela in Mandela: Long Walk To Freedom and best actor in a mini-series or TV movie category for his role as the troubled detective in the BBC's Luther.
Ejiofor was nominated in the same category for another BBC drama - Dancing On The Edge - while his role in McQueen's epic 12 Years A Slave got him a nod for best actor in a motion picture.
The film is based on the true story of New Yorker Solomon Northup who was kidnapped and sold into slavery as an adult.
But there was one blow for the film after McQueen lost out on the battle for best director to Alfonso Cuaron and his space adventure Gravity.
American Hustle was another key winner of the night, taking home best motion picture for a musical or comedy.
Jacqueline Bisset was Britain's only female to triumph, winning best supporting actress in a series, mini-series or movie for the BBC's Dancing On The Edge, beating fellow Brit and White Queen star Janet McTeer.
The nominees for best actress in a motion picture drama read like a roll call of UK acting talent with nods for Emma Thompson in Saving Mr Banks, Kate Winslet in Labor Day and Dame Judi Dench for Philomena.
But the acclaimed actresses were all left behind after Cate Blanchett took home the gong for her role in Blue Jasmine.
Helena Bonham-Carter also missed out after a nomination for best actress in a mini-series for her starring role in the BBC Four TV film Burton And Taylor.
Writers Jeff Pope and Steve Coogan watched on as their hit film Philomena lost out to futuristic romance Her, written by Spike Jonze, in the best screenplay category.
Nominee Christian Bale was left empty handed after Leonardo DiCaprio took home the Golden Globe for best actor in a comedy or musical for The Wolf Of Wall Street.
Bale was shortlisted for his starring role as conman Irving Rosenfeld in American Hustle.
Blue Jasmine star Sally Hawkins lost out in the best supporting actress category to Jennifer Lawrence, who collected the award for her role in American Hustle in another win for the blockbuster.
U2 and Danger Mouse won the award for best original song for Ordinary Love, in the Nelson Mandela biopic Mandela: Long Walk to Freedom - the band's first recording since 2010.
U2 singer Bono said working on the film completed a decades-long journey with Mandela, having played an anti-apartheid concert some 35 years ago.
"This man turned our life upside down, right-side up," said Bono of the South African leader who died last month.
"A man who refused to hate not because he didn't have rage or anger or those things, but that he thought love would do a better job."
It meant Coldplay missed out with their chart hit Atlas for the US blockbuster Hunger Games: Catching Fire.
Despite its latest series breaking audience records on the other side of the pond, ITV's Downton Abbey failed to win best TV series drama after coming up against the gritty Breaking Bad.
The Los Angeles awards show, organised by the Hollywood Foreign Press Association (HFPA), is seen as a pointer for who will challenge for Oscars honours in March.
After 12 Years A Slave missed out on six of the seven categories it was nominated in, director McQueen was surprised it won best film drama at the end of the night.
"A little bit in shock," he said, before shrugging "Roll, Jordan, roll" - the lyrics to the old gospel song sung in the slavery epic.
Prime Minister David Cameron was among the first to congratulate the team behind the film, tweeting: "Congratulations to everyone involved with the British film "12 Years a Slave" -which did so well at the #GoldenGlobes."