Writers Steve Coogan and Jeff Pope accepted the accolade during Sunday's award ceremony in London, with Coogan praising the "real Philomena Lee" who was present in the audience.
Philomena tells the story of an Irish woman's search for the son she was forced to give up for adoption.
Coogan 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".
It was a night of disappointment for NI screenwriters Colin Carberry and Glenn Patterson who did not pick up the prize in the outstanding debut by a British writer, director or producer category.
They were nominated for their debut feature Good Vibrations which depicts the life of Belfast godfather of punk Terri Hooley.
Meanwhile 12 Year A Slave was the big winner on the night, receiving the much sought after awards for best film and best leading actor for its star Chiwetel Ejiofor.
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 said he was "so deeply honoured and privileged to receive it" and thanked McQueen for his "artistry and passion".
He added: "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".
Sunday's other big contender, Gravity, won six Baftas including outstanding British film and best director for Mexican film-maker Alfonso Cuaron.
Accepting his award, Cuaron said: "You cannot 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".
Jennifer Lawrence won best supporting actress for her role in American Hustle, while Cate Blanchett picked up the prize for best leading actress for Woody Allen's latest movie Blue Jasmine.
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".
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".
List of main Bafta winners:
Best Film: 12 Years A Slave
Leading Actor: Chiwetel Ejiofor
Leading Actress: Cate Blanchett
Director: Alfonso Cuaron for Gravity
Supporting Actor: Barkhad Abdi for Captain Phillips
Supporting Actress: Jennifer Lawrence for American Hustle
Fellowship: Dame Helen Mirren
Outstanding Contribution: Peter Greenaway
Outstanding British Film: Gravity
Adapted Screenplay: Jeff Pope and Steve Coogan for Philomena
Original Screenplay: Eric Warren Singer and David O.Russell for American Hustle
Original Music: Gravity