"Argo" won the award, which the First Lady read off an envelope while being paged in to Los Angeles' Dolby Theatre.
"[These films] taught us that love can beat all odds," Obama said. "They reminded us that we can overcome any obstacle if we dig deep enough and fight hard enough and find the courage within ourselves."
It's through cinema, Obama said, that "our children learn to open their imagination and dream just a little bigger and to strive every day to reach those dreams."
"Argo's" win was remarkable because it was only the fourth film in the Oscars' 85-year history to win Best Picture without a corresponding Best Director nomination. Affleck, a producer on the film, gave an emotional acceptance speech that ended with a simple message: "It doesn't matter how you get knocked down in life, all that matters is how you get back up."