Jack Nicholson presented the award with the help of first lady Michelle Obama, who appeared via streaming video from the White House.
Among the many people Affleck thanked in his emotional acceptance speech were the film's real-life protaganist Tony Mendez and his wife, actress Jennifer Garner, in his acceptance speech.
"I want to thank our friends in Iran, living in a terrible circumstances right now, I want to thank my wife, who I don't normally associate with Iran," he said. "I want to thank you for working on our marriage for 10 Christmases. It's good. It is work but it's the best kind of work, and there's no one I'd rather work with."
Get the full list of 2013 Oscar winners
Daniel Day-Lewis won his third Oscar in the best actor category, this time for his role as "Lincoln," while Jennifer Lawrence won her first Oscar for best actress for "Silver Linings Playbook." The 22-year-old actress tripped on her way to the stage as the crowd gave her a standing ovation.
"You guys are just standing up because you feel bad that I fell," Lawrence joked.
Anne Hathaway won her first Oscar for her supporting role in the musical "Les Miserables." She accepted her award saying simply, "It came true." It was just two years ago that Hathaway hosted the Oscars with James Franco. She is the third performer in a musical to win supporting actress during the genre's resurgence in the last decade.
Hathaway acknowledged her competitors for supporting actress, including Helen Hunt, Amy Adams, Jacki Weaver and Sally Field.
"I look up to you all so much, and it's just been such an honor, thank you," she said.
After a mildly edgy opening monologue by Oscar host Seth MacFarlane, the first award of the night was given to Christoph Waltz for best actor in a supporting role for "Django Unchained." It was Waltz's second supporting actor Oscar for a Quentin Tarantino film. He won in 2009 for playing a gleefully evil Nazi in "Inglourious Basterds."
In a choked voice, Waltz offered thanks to his character and "to his creator and the creator of his awe-inspiring world, Quentin Tarantino."
MacFarlane started the show poking fun at the Academy for snubbing Ben Affleck, who was not nominated for best director for "Argo."
"The story was so top secret that the film's director is unknown to the academy," MacFarlane said. "They know they screwed up. Ben, it's not your fault."
The best director award was given to Ang Lee for "Life of Pi." It was the second Oscar for Lee, who won in 2005 for "Brokeback Mountain."
The Scottish adventure "Brave," from Disney's Pixar Animation unit, was named best animated feature. Pixar films have won seven of the 12 Oscars since the category was added.
All final preparations were finished Sunday morning for the huge extravaganza. Producers behind the show say 20,000 people from all over the world applied to sit in the bleachers alongside the red carpet, but only 700 lucky fans snagged tickets.
Naomi Watts turned heads wearing an Armani Prive gown and Neil Lane jewelry, while Jennifer Aniston looked glamorous in a Valentino red strapless gown. Fans cheered as their favorite celebrities walked the red carpet.
Amy Adams arrived wearing a gown by Oscar de la Renta. This is the fourth Oscar nomination for the 38-year-old actress.
"It was just a magical experience," she said. "I love what I do, and I love the people I work with, so it's nice to be acknowledged by the community."
The Associated Press contributed to this report.
