"You know, there's one place with all the people with the greatest potential are gathered, and that's the graveyard," she said. "People ask me all the time, 'What kind of stories do you want to tell, Viola?' And I say, exhume those bodies, exhume those stories. The stories of the people who dream big and never saw those dreams to fruition. People who fell in love and lost."
August Wilson, who wrote the play from which "Fences" is adapted, was among the people she thanked.
"Here's to August Wilson who exhumed and exalted the ordinary people," Davis said.
Davis also thanked her husband and her daughter, saying they "teach me every day how to live, how to love."
"I'm so glad you are the foundation of my life," she added.
"Oh captain, my captain. Denzel Washington," she said. "Thank you for putting two entities in the driving seat, August (Wilson) and God, and they served you well."
Washington wished Davis luck from the red carpet before the show. He played Davis' husband in the film, which is also nominated for best picture and best adapted screenplay.
"I really think this is her time, her turn," he told Robin Roberts of "Good Morning America."
Davis made history earlier this year by becoming the first African-American woman nominated for three Academy Awards. She was previously nominated for her roles in "The Help" (2011) and "Doubt" (2008).
"I became an artist and thank God I did," she said, "because we are the only profession that celebrates what it means to live a life."