She also made history by being the first female recipient of the best director title.
Bigelow dedicated her award to “never abandoning the need to find a resolution for peace”.
After picking up best film award presented by Dustin Hoffman, she said: “This is so unbelievable, we’re just so deeply honoured and humbled.”
She said the film had put “a bit of a spotlight on a very, very difficult situation”.
Twilight heart-throb actor Robert Pattinson presented the original screenplay award to Mark Boal.
Boal said: “This is really a wonderful honour. I was very fortunate on this picture to have tremendous actors.
“I’d like to thank them for this and also Kathryn Bigelow. It was an unpopular story about an unpopular war.”
Colin Firth was recognised at the Orange British Academy Film and Television Awards, as the Baftas are formally known, for his portrayal of a gay academic battling grief in A Single Man.
“What Tom Ford doesn’t know is I have the email in my outbox telling him I could not possibly do this,” he said.
“I was about to send this when a man came to repair my fridge... I don’t know what’s best for me so I would like to thank the fridge guy.”
He thanked Ford who “knows what’s best for me. An encounter with Tom Ford is to come away feeling resuscitated, a little more worldly, better groomed, more fragrant, and more nominated than one has ever been before.
“I have worked with a lot of great directors and he’s up there with the best of them.
“All I know is don’t ever press ‘send’ until you have had your fridge repaired.”
After winning the supporting actor gong for his role as a Nazi in Inglourious Basterds, Austrian Christoph Waltz paid tribute to Quentin Tarantino for getting him to play a Nazi in an unstereotypical way.
He said: “It is utterly boring to have this stereotypical beast polluting movie screens and TV because they were human beings and that was what made them dangerous. Finally we had someone who took a realistic approach, it took Quentin.”
“I lived in London for 20 years and I struggled. I was a struggling actor in London, I did the odd job but I had to go back to Germany to work to make a living.
“Coming back for this is unbelievable.”
US Twilight actress Kristen Stewart, who beat her British counterparts to the Rising Star award, said: “I’m sat right behind Kate Winslet and every time she turns around I feel I wish I didn’t exist. I love her.”
Carey Mulligan had to fight back tears backstage after landing best actress for An Education.
“I’m going to cry. (It means) everything. (I’m going to) burst into tears”.