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.
Jennifer Lawrence tripped over the long train of her gorgeous gown on her way to scoop up the Best Actress statuette for her performance in "Silver Linings Playbook."
"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.
Writer-director Quentin Tarantino picked up the Oscar for Best Original Screenplay for "Django Unchained," while that film's scene-stealer Christoph Waltz was declared Best Supporting Actor. Waltz previously won the Oscar in the same category for his work in another Tarantino flick, "Inglourious Basterds."
Anne Hathaway earned the Best Supporting Actress Oscar for her performance in "Les Miserables." The movie musical won the awards for Sound Mixing, and Hair and Makeup, as well.
Adele took home the Best Original Song Oscar for the title theme to "Skyfall," the latest James Bond adventure, which shared the Sound Editing Oscar with "Zero Dark Thirty."
"Brave" was declared Best Animated Feature and "Paperman" Best Animated Short.
The Best Costume Design honor went to "Anna Karenina" and "Amour" earned the Best Foreign Language Film title.
Obama was wearing a Naeem Khan when she announced "Argo" had won live from the Diplomatic Room of the White House. She had just come from a National Governors Association dinner at the White House.
Obama's role as an Oscar presenter had been kept a top secret.
"The Academy Awards approached the first lady about being a part of the ceremony," Kristina Schake, Obama's communications director, said in a statement.
"As a movie lover, she was honored to present the award and celebrate the artists who inspire us all -- especially our young people -- with their passion, skill and imagination."