The film's fourth award, for best supporting actor, went to Spain's Javier Bardem for playing a killer of few words.
In other top awards, members of the Academy of Motion Picture Arts and Sciences honored a wide range of movies, actors and actresses from several countries, highlighting a recent trend toward globalization in cinema.
But Hollywood's biggest night belonged to the Coens -- offbeat filmmakers who have shown a skill at taking what could be mundane stories, populating them with quirky characters and looking at troubling questions of human frailty.
Accepting his Oscar, Joel Coen talked about how he and Ethan had made films since they were kids and said his brother had taken a camera to the airport as a boy in the 1960s to create "Shuttle Diplomacy: Henry Kissinger Man on the Go."
"Honestly, what we do now doesn't feel that much different from what we did then," he joked.
Briton Daniel Day-Lewis won for best actor as a sadistic oil prospector in the early 20th century whose rise to wealth and power comes at a deep cost to his soul. He was heavily favored for an Oscar after winning a series of other industry awards for the role.
Another British performer, Tilda Swinton, took supporting actress honors as a shifty lawyer in the thriller "Michael Clayton" and France's Marion Cotillard was named best actress for portraying singer Edith Piaf in "La Vie en Rose."
These Oscars marked the first time since 1964 that the top four acting awards went to non-Americans, and Cotillard was the first French woman to win best actress since 1960.
"I'm speechless now," Cotillard said on stage, visibly surprised and overjoyed. "Thank you life, thank you love. It is true there (are) some angels in this city."
Bardem took the occasion to thank his family in Spanish, apologizing in advance to the Hollywood audience. "This is for Spain and this is for all of you," he said.
The Austrian Holocaust-era drama "The Counterfeiters" won the Oscar for best foreign language film. Directed by Stefan Ruzowitzky, it was the first win for Austria in the category.
In other key categories, best animated film went to audience favorite and box office hit "Ratatouille" about a friendly rat who becomes a chef in a Parisian kitchen.
Best original screenplay went to stripper turned writer Diablo Cody for the hopeful teen pregnancy comedy "Juno."
Despite the talk of dark and pessimistic movies at this year's Oscars, many winners offered statements of optimism. Perhaps the most inspiring came from Marketa Irglova who, along with Glen Hansard, won for best original song with the tune "Falling Slowly" from the low-budget movie "Once."
Until the film won over audiences, Irglova and Hansard were unknown.
"This is just a proof that no matter how far out your dreams are, it's possible," said Irglova. "This song was written from a perspective of hope and hope connects us all."
Director Alex Gibney of documentary winner "Taxi to the Dark Side" -- a look at the use of torture by the United States -- also offered a message of optimism. "Let's hope we can turn away from the dark side and return to the light," Gibney said.
Political satirist Jon Stewart returned as Oscar host and, in his opening monologue, made light of that pessimistic tone of many of the best film nominees.
"Does this town need a hug? What happened?" Stewart said. What happened? Oscar hugged the Coens.