A granddaughter of Frank Lloyd Wright, Baxter studied acting with Maria Ouspenskaya and had some stage experience before making her film debut in "20 Mule Team" (1940). She became a contract player of 20th Century Fox and was loaned to RKO Pictures for the role of Lucy Morgan in Orson Welles' "The Magnificent Ambersons" (1942), one of her earlier films. In 1947, she won the Academy Award for Best Supporting Actress for her role as Sophie MacDonald in "The Razor's Edge" (1946). In 1951, she received an Academy Award nomination for Best Actress for the title role in "All About Eve" (1950). She worked with several of Hollywood's greatest directors, including Billy Wilder in "Five Graves to Cairo" (1943), Alfred Hitchcock in "I Confess" (1953), Fritz Lang in "The Blue Gardenia" (1953), and Cecil B. DeMille in "The Ten Commandments" (1956).