Stanley starred in such Broadway hits as Picnic and Bus Stop. A savaging by London critics of a performance she did in The Three Sisters made her vow never to perform on the stage again, and she kept that vow for the rest of her life.
Her first film was The Goddess in 1958. In 1964 she starred in Seance on a Wet Afternoon, for which she was nominated for the Academy Award for Best Actress. Other films include Frances, for which she was nominated for the Academy Award for Best Supporting Actress, and The Right Stuff.