The movie also earned the awards for Best Adapted Screenplay and Film Editing earlier at the high-profile ceremony in Los Angeles.
In accepting the evening's top prize, "Argo" producer Grant Heslov said he wanted to take the microphone before Affleck spoke, noting it might be awkward for the actor-producer-director to thank himself for all his fine work.
"But it's not awkward for me," Heslov said. "Thank you, Ben. You directed a hell of a film."
Affleck, who wasn't nominated for a Best Director Oscar even though he won numerous prizes in other competitions for directing "Argo," was clearly emotional as he accepted the Best Picture honor.
"I was here 15 years ago and I had no idea what I was doing," Affleck said, referring to the Oscar he and friend Matt Damon won for penning the screenplay for "Good Will Hunting." "I was a kid. I never thought I would be back here and now I am because of so many of you."
Ang Lee earned the Best Director accolade for his work on "Life of Pi," which also won the Oscars for Best Cinematography, Visual Effects and Original Score.
"Thank you, movie God!" Lee said, smiling as he collected his Best Director Oscar.
"You guys are just standing up because you feel bad that I fell and that's really embarrassing, but thank you," she told the crowd. "This is nuts! Thank you to the Academy [of Motion Picture Arts and Sciences] and thank you to the women this year, you were so magnificent. You were so inspiring and not just those of you in my category; and it's been so amazing getting to know you and you've been so nice and you've made this experience unforgettable."
Daniel Day-Lewis took home an unprecedented third Best Actor Oscar for his work in "Lincoln," which led the field with 12 nominations, but only won one other award -- for Best Production Design -- Sunday night.