"It doesn't escape me for one moment that so much joy in my life is thanks to so much pain in someone else's," she said. "It has been the joy of my life."
Nyong'o plays a tortured slave girl in the historical drama directed by Steve McQueen. It was her first Oscar nomination and win.
"I am certain that the dead are standing about you and watching, and they're grateful, and so am I," Nyong'o said to McQueen.
The first award of the night went to Jared Leto for best supporting actor in "Dallas Buyers Club."
"Incredible," Leto said as he took the stage. It was also his first Oscar nomination and win.
He plays a transsexual in the Texas AIDS drama starring Matthew McConaughey. Leto dedicated the award to his mother, a "high school dropout and a single mom" who made a better life for herself and her children.
"She encouraged her kids to be creative, to work hard, and to do something special," Leto said. "Thank you for teaching me to dream."
The 86th Oscars kicked off with a hilarious opening monologue by host Ellen DeGeneres, who teased Jennifer Lawrence for falling last year while accepting her Oscar, and then falling again Sunday on the red carpet.
"If you win tonight, I think we should bring you the Oscar," said DeGeneres to Lawrence, nominated for best supporting actress for "American Hustle."
DeGeneres also got big laughs from the crowd when she said to Jonah Hill, "You showed us something in that film that I have not seen for a very, very long time," alluding to his nude scene in "Wolf of Wall Street."
The best director award went to Mexican filmmaker Alfonso Cuaron for the 3-D space spectacle "Gravity." He is the first Latino to win the category.
Disney's "Frozen" won best animated film, marking the studio's first win in the 14 years of the best animated feature category. The film's "Let It Go" won best original song.
After a torrential downpour swept through Los Angeles over the weekend, Oscar crews scrambled to get ready for the glamorous award show. As skies began to clear, the red carpet was uncovered for arrivals.
Lawrence arrived in a red hot Dior dress, while Nyong'o looked stunning in a light blue Prada gown with a deep V-neck top. She said the color reminded her of her Kenyan home.
"I'm living a dream," she told ABC7 Entertainment Guru George Pennacchio. "I'm looking forward to what's going to come after this."
"12 Years a Slave," "Gravity" and the con-artist caper "American Hustle" are vying for best picture in the night's closest contest. "Gravity" is expected to lead the ceremony in total awards, cleaning up in technical categories like visual effects and cinematography.
The Associated Press contributed to this report.