Page was born on November 22, 1924 in Kirksville, Missouri. Her family relocated to Chicago when she was five and there she was introduced into acting through a local church. After graduating from Chicago's Englewood Technical Prep Academy, she attended the Goodman School of Drama at the Art Institute of Chicago (now at DePaul University), with the intention of becoming a visual artist or pianist. She found her way to the American Theatre Wing in New York City, studying with Uta Hagen for seven years, and then at the Actors Studio with Lee Strasberg. While attempting to establish her career, she worked various odd jobs, including as a hat-check girl, theater usher, lingerie model, and a factory laborer.
She made her stage debut in 1945 with the play Seven Mirrors. It led to many other prominent Tony Award nominated roles in shows, like Absurd Person Singular, Agnes of God, Blithe Spirit, The Rainmaker, A Streetcar Named Desire, The Little Foxes, Mid-Summer, The Innkeepers, Separate Tables, P.S. I Love You, Angela, Clothes for a Summer Hotel, and Sweet Bird of Youth, where she would also reprise the stage role for the 1962 film adaptation.
Her other film credits include Hondo, Summer and Smoke, Toys in the Attic, Dear Heart, You're a Big Boy Now, The Three Sisters, Trilogy, Whatever Happened to Aunt Alice?, Pete 'n' Tillie, Interiors, The Pope of Greenwich Village, Riders to the Sea, and A Trip to Bountiful, which won her the Academy Award for Best Actress.
Page also made appearances in television shows, like Omnibus, General Electric Theater, Playhouse 90, Night Gallery, The Name of the Game, Kojak, Hawaii Five-O, Ghost Story, and Medical Center. She also appeared in television films, like The Thanksgiving Visitor, Look Homeward, Angel, Something for Joey, The Blue and the Gray, The Dollmaker, The Parade, and Nazi Hunter: The Beate Klarsfeld Story.
On June 13, 1987, Page failed to arrive at the Neil Simon Theatre for both the afternoon and evening performances of Blithe Spirit. At the end of the show's evening performance, the play's producer announced that Page had been found dead in her lower Manhattan townhouse. It was determined that she died of a heart attack. After her funeral, Page was cremated.