It won the leading actor award for its star Chiwetel Ejiofor and was named best film.
Its director Steve McQueen accepted the best film gong and thanked his "one and only mother for having the faith, never give up".
He told the audience: "There are 21 million people in slavery as we sit here. I just hope 150 years from now our ambivalence will not allow another film-maker to make this film".
Ejiofor, who accepted his award from Uma Thurman, said he was "so deeply honoured and privileged to receive it" and thanked McQueen for his "artistry and passion".
He said: "You really brought us all through it and had the real vision to tell this extraordinary story".
"Thank you for this. This is yours by the way, I know that, you know that. I'm going to keep it but it's yours".
At one point it had looked like outer-space drama Gravity was going to sweep the board. It won six Baftas including outstanding British film and best director for Mexican film-maker Alfonso Cuaron who beat the much-fancied McQueen to the award.
Accepting his award, Cuaron said: "You can not tell from my accent but I consider myself a part of the British film industry".
Telling the audience, he had made "almost half" of his films in the UK, he joked: "I guess I'm a very good case for curbing immigration"
Gravity, which stars US actors Sandra Bullock and George Clooney, has caused some controversy by being listed as a British film but it was filmed in this country and the team responsible for its visual effects are UK-based.
The night ended with the honorary fellowship award for Dame Helen Mirren which was presented by the Duke of Cambridge who described her as "an extremely talented British actress who I should probably call granny".
Accepting her award, Dame Helen paid her own tribute to one of her former teachers, Alys Welding, who died recently and "alone was the person who encouraged me to be an actor".
She ended by quoting from William Shakespeare's The Tempest, saying: "'We are such stuff as dreams are made on and our little life is rounded with a sleep'
"My little life is rounded with this honour, thank you very much indeed."
Speaking backstage, she said William had been "charming".
Cate Blanchett was named best actress for her role in the Woody Allen film Blue Jasmine.
She dedicated her win to Philip Seymour Hoffman, who died earlier this month in New York, calling him "a continual profound touchstone".
She said: "Phil, buddy, this is for you, you bastard. I hope you're proud."
The night had begun with some of the biggest stars of Hollywood on the red carpet outside the Royal Opera House in Covent Garden, central London.
Fans lined up alongside the red carpet to get a glimpse of celebrities including Amy Adams, Eddie Redmayne and Martin Scorsese.
Gillian Anderson, the star of The Fall and The X-Files, posed for photographers in a vintage 1949 dress, while Luther star Ruth Wilson was dressed more for the chilly evening weather in a silver suit.
Another of the stars 12 Years A Slave, Lupita Nyong'o, posed for pictures on the red carpet in an emerald green Dior dress with matching shoes.
The event, formally known as the EE British Academy Film Awards, was hosted by Stephen Fry and broadcast on BBC1.
Among the outfits turning heads were Amy Adams in a flowing black Victoria Beckham design, while at the other end of the scale, singer Lily Allen went for a bright pink and orange dress with pink feathers in her hair.
One of the biggest cheers of the night was reserved for Brad Pitt and Angelina Jolie who arrived together wearing matching tuxedos.
Welcoming the audience, Fry paid tribute to Dame Helen joking that the actress - who has played the Queen on stage and screen - has "this year brought her grandson along. Welcome his Royal Highness the Duke of Cambridge".
The ceremony opened with a performance by Tinie Tempah and Laura Mvula, before Oprah Winfrey handed the award for outstanding British film to Gravity.
Gravity won its second award of the night when it picked up the Bafta for sound and it triumphed again winning the Bafta for original music.
Emma Thompson presented the award for supporting actor to Barkhad Abdi for his role as a Somalian pirate in Captain Phillips.
Accepting his award, he thanked his co-star Tom Hanks, his "fellow pirates" and film maker Paul Greengrass for "for believing in me before I believed in myself".
Gravity picked up another award with the Bafta for cinematography before the supporting actress gong was given to Jennifer Lawrence for American Hustle with the film's director, David O. Russell, accepting it on her behalf.
Film-maker Peter Greenaway, whose career includes art-house hits such as The Cook, The Thief, His Wife and Her Lover, was then presented with the outstanding contribution award by Juliet Stevenson who said "he has no time for convention or orthodoxy"
Accepting his award, Greenaway said he was "very, very surprised" to receive it and thanked those who "travel with me".
The award for original screenplay went to US 1970s crime caper American Hustle.
Eric Warren Singer, who accepted the award with Russell, said: "I was breastfed from a very young age on British cinema, so thank you Bafta".
Steve Coogan and Jeff Pope won the award for adapted screenplay for Philomena - the story of an Irish woman's search for the son she was forced to give up for adoption.
Accepting the award, Coogan praised the "real Philomena Lee".
He said: "Her story has been told and her story finished in the Vatican. She has been heard but there are 60,000 women who are yet to trace their children".
Will Poulter won the EE Rising Star award which is based on a public vote, before the Bafta for special visual effects went to Gravity.