Brave, the Disney fantasy set in the Highlands, was named Best Animated Film, and Glasgow director Lynne Ramsay took Best Short Film for Swimmer.
Will Anderson from Inverness and Ainslie Henderson from Edinburgh added to the Scottish success in the Short Animation category for The Making Of Longbird.
Featuring a host of Scottish actors' voices, Brave won a Golden Globe last month and has also been nominated in the the Oscars.
The movie, which has been hailed as a major boon for Scottish tourism, follows the heroic journey of Merida, voiced by Kelly Macdonald. Other actors involved include Billy Connolly, Emma Thompson, Kevin McKidd, Craig Ferguson and Robbie Coltrane.
Ramsay, 43, who is married to Rory Kinnear, is best known for the feature films Ratcatcher, Morvern Callar and We Need to Talk about Kevin. She
Swimmer, shown on BBC TV, was commissioned as part of the Olympic festival, one of four short films by British directors.
It is described as a poetic journey through the waterways and coastline of the British Isles, following a lone swimmer through lakes, rivers and coves. The journey is framed by a soundtrack of seminal British music.
Elsewhere, the main early Bafta winner was Skyfall, named Outstanding British Film of the year.
The movie, the third starring Daniel Craig as the suave spy, is already the highest-grossing film of all time at the UK box office.
The Bafta award was presented by Bradley Cooper and Ben Affleck. Skyfall also won Best Original Music for Thomas Newman.
Director Sam Mendes paid tribute to the "bravery and brilliance" of Craig and "the great" Ian Fleming, who created James Bond.
Speaking backstage, Mendes said he would love to make another Bond film.
He told reporters: "I've had a great time, it's been a huge learning curve and we would want to make a better movie next time around, and if we thought we do that they might let me have another go again."
Lincoln star Sally Field came on stage to present the award for Original Screenplay without her presenting partner Eddie Redmayne after he was taken ill backstage.
Field told the audience: "He seems to be puking his guts out back there."
Quentin Tarantino picked up the award for his western Django Unchained and thanked his actors for doing a "bang-up job with my dialogue".
The film has attracted criticism for its liberal use of racial insults and Tarantino thanked his backers for standing by what he described as "a hot potato" film.
Hunger Games star Jennifer Lawrence handed the award for Best Supporting Actor to Christoph Waltz for Django Unchained.
Accepting his award, he said it was an "immense honour" and paid tribute to its "silver-penned" writer.
He said: "Why I get to stand here is really no mystery because it says at the beginning of our film, 'written and directed by Quentin Tarantino'."
Speaking backstage, Tarantino said he saw Django Unchained as the second part in a trilogy following on from his Second World War film Inglourious Basterds.
He said both films were about righting the wrongs of history, adding: "I think there's something about this that begs a trilogy, three movies that go on this train and then drop it. I don't know what the third one's going to be yet."
Billy Connolly came on stage to present the award for an Outstanding Debut by a British Writer, Director or Producer.
Joking that he was "presenting an unsuspecting stranger with a deathmask on a stick", the comedian and actor gave the award to Bart Layton and Dimitri Doganis for their documentary The Imposter.
The film tells the true story of Frenchman Frederic Bourdin, who posed as a missing Texan teenager so successfully that he moved in with his family and lived as him for several months.
The next award, for Special Visual Effects, went to the 3D spectacular Life Of Pi.
George Clooney presented the award for Supporting Actress to Les Miserables star Anne Hathaway.
The actress thanked the "golden-hearted group" who made the film and wished her co-star Redmayne well, saying: "Feel better. I mean I'd be holding your hair back, but, you know..."
She also thanked Victor Hugo - the writer of the original novel which inspired the musical - saying: "Without whom, none of us would be here."
The award for Best Adapted Screenplay went to David O Russell for Silver Linings Playbook.
Trainspotting director Danny Boyle presented the award for Outstanding British Contribution to Cinema to FilmFour boss Tessa Ross, who he described as a "shy genius".
He said: "I can pay her no greater compliment than to say she really is the Paul Scholes of the British film industry."
The award for Film Not in the English Language went to Amour.
The EE Rising Star Award - which is voted for by the filmgoing public - went to Juno Temple.
The actress, who starred in Killer Joe, said it was "a huge, huge honour" to win and thanked her brother, Felix, who she said "got his entire school to vote for me".
She also thanked her father, film-maker Julien Temple, for inspiring her to act.
Martin Freeman joined Henry Cavill on stage to present the award for Best Documentary to Searching for Sugarman - the story of two music fans looking for a little known American musician called Rodriguez whose career has been revived by the film's success.
The award for Production Design went to Eve Stewart and Anna Lynch-Robinson for their work on Les Miserables.
Ben Affleck was named Best Director by Ian McKellen for his work on Argo, and the the movie also took best film, beating pre-event favourite, Lincoln.
Affleck, who rose to fame as an actor, said: "I want to say this is a second act for me and you've given me that, this industry has given me that and I want to thank you and I'm so grateful and proud."
Emmanuelle Riva was named Best Actress for her performance in Amour and Daniel Day-Lewis won the Best Actor award.
He accepted the award and poked fun at his own reputation for immersing himself in his characters and his devotion to method acting.
Day-Lewis, who reportedly refused to leave his wheelchair while playing the disabled Christy Brown in My Left Foot, said: "On the chance I might one day have to speak on an evening such as this I've stayed in character as myself for the last 55 years".
Sir Alan, who made films including Midnight Express and Bugsy Malone during a long career, said the lifetime achievement award was "incredibly flattering".
He said: "When you're halfway through your first film you're sure it's going to be your last then you blink and 40 years have gone by and you've made 14 films."
Outstanding British Film - Skyfall
Animated Film - Brave
Original Screenplay - Django Unchained (Quentin Tarantino)
Original Music - Skyfall (Thomas Newman)
Cinematography - Life Of Pi (Claudio Miranda)
Editing - Argo (William Goldenberg)
Costume Design - Anna Karenina (Jacqueline Durran)
Make-up and Hair - Les Miserables (Lisa Westcott)
Sound - Les Miserables
Short Animation - The Making Of Longbird
Short Film - Swimmer
Bafta Fellowship - Sir Alan Parker
Outstanding British Contribution to Cinema - Tessa Ross
Best Film - Argo
Outstanding Debut by a British Writer, Director or Producer - Bart Layton, Dimitri Doganis (The Imposter)
Film Not in the English Language - Amour
Documentary - Searching For Sugar Man
Director - Ben Affleck (Argo)
Adapted Screenplay - David O Russell (Silver Linings Playbook)
Leading Actor - Daniel Day-Lewis (Lincoln)
Leading Actress - Emmanuelle Riva (Amour)
Supporting Actor - Christoph Waltz (Django Unchained)
Supporting Actress - Anne Hathaway (Les Miserables)
Production Design - Les Miserables (Eve Stewart, Anna Lynch-Robinson)
Special Visual Effects - Life Of Pi
EE Rising Star Award (voted for by the public)- Juno Temple