The actor beat off competition from other UK hopefuls - the category favourite Sir Ian McKellen for Lord of the Rings, and Sir Ben Kingsley for Sexy Beast.
Dame Judi Dench was also nominated for her role as the writer Murdoch, but the best actress Oscar was handed to Halle Berry for her performance in Monster's Ball.
And Tom Wilkinson was another British actor who walked away empty-handed after Denzel Washington was named as the surprise best actor winner.
Another success for the UK was Julian Fellowes, writer of Gosford Park, who won best original screenplay.
"I feel as if I'm in A Star is Born - my thanks start with the great Robert Altman who's given me the biggest break into movies," he said.
"When I'm not working I'm mean, moody and difficult and when I start working I become someone who's become even more mean, moody and difficult. Thankyou very much and God bless America."
Breaking the habit
Earlier in the evening three UK actresses missed out on awards after the best supporting actress Oscar went to Jennifer Connelly for A Beautiful Mind.
Connelly beat Broadbent's Iris co-star Kate Winslet, and Gosford Park's Dame Maggie Smith and Helen Mirren.
As Winslet arrived at the ceremony with boyfriend Sam Mendes, she had joked: "This is the third time I've been nominated and it would be a shame to break a habit if I won."
Music veterans Sting and Sir Paul McCartney lost out to Randy Newman for Monster's Inc in the original score category.
Sir Paul was nominated for his music in the thriller Vanilla Sky, while Sting's track was used in comedy Kate and Leopold.
Tom Wilkinson has yet to hear whether he will win for best actor.
The number of UK acting nominees this year is an improvement on 2001, when just three - Julie Walters, Dame Judi Dench and Albert Finney - were up for awards.
All ended up missing out, however, along with UK director Ridley Scott for Gladiator.
Praise
This was Dame Judi's fourth Oscar nomination in five years. And Wilkinson's performance in the American drama In the Bedroom had been widely praised.
Rivals
Britain had an early win in one of the technical categories, when Peter Owen shared the best make-up prize with Richard Taylor for Lord Of The Rings.
Briton Jenny Beavan, who worked on Gosford Park, lost out in the best costume design category to Moulin Rouge designers Catherine Martin and Angus Strathie.
And Gosford Park art directors Stephen Altman and Ann Pinnock were also beaten to an Oscar in their field by Ms Martin, wife of Moulin Rouge director Baz Luhrmann.
And UK director Ridley Scott lost out on best director for his war movie Black Hawk Down, to Ron Howard and A Beautiful Mind.