"I read an article that said that winning an Oscar could lead to living five years longer. If that's true, I'd really like to thank the academy because my husband is younger than me," Moore joked in her acceptance speech.
She went on to thank her fellow nominees, noting, "There's no such thing as best actress." She thanked her family, manager, costars and Sony Pictures Classics.
FULL COVERAGE: Oscars 2015
The Oscar comes on the heels of Moore’s
"I'm thrilled actually that we were able hopefully to shine a light on
Though this is her first Oscar, Moore has won three Golden Globes, two SAG Awards and one Emmy.
Moore faced fierce competition in the category from Reese Witherspoon for her performance as Cheryl Strayed in "Wild," Felicity Jones for her performance as Jane Wilde-Hawking in "The Theory of Everything," Rosamund Pike for her performance as Amy Dunne in "Gone Girl" and Marion Cotillard for her performance as a working-class mother lobbying to keep her job in "Two Days, One Night."