Page was born in Kirksville, Missouri, where her father, Leon Page (author of Practical Anatomy (1925), Osteopathic Fundamentals(1926) and The Old Doctor (1932)) was on the faculty of the Andrew Taylor Still College of Osteopathy and Surgery (combined with the American School of Osteopathy, eventually to form ATSU). After graduating from Chicago's Englewood High School, she attended the Goodman School of Drama (later renamed The Theatre School at DePaul University) in Chicago and studied acting with Uta Hagenin New York.
Page was a trained Method actor and worked closely with Lee Strasberg. She began appearing in stock theatre at 17. In 1952, her appearance as Alma Off-Broadway revival of Tennessee Williams' Summer and Smoke at the downtown Circle in the Square Theatrewas legendary. Page's performance (as the minister's daughter consumed with infinite longing) in the 1952 production, directed byJosé Quintero, gave the play a new life, and, according to common wisdom, it was that production (for its daring, for its fervor, for its being "downtown" rather than in the artistically "safe" realm of Broadway) which gave birth to the Off-Broadway movement in New York theatre. Her work continued on Broadway as the spinster in The Rainmaker, and as the frustrated wife whose husband becomes romantically obsessed with a young Arab, played by James Dean, in The Immoralist.
She earned critical accolades for her performance in Tennessee Williams' Sweet Bird of Youth opposite Paul Newman. She originated the role of a larger-than-life, addicted, sexually voracious Hollywood legend trying to extinguish her fears about her career with a young hustler named Chance Wayne, played by Newman. Page received her first Tony Award nomination for the play, as well as the Sarah Siddons Award for her performance in Chicago. She and Newman later starred in the film adaptation and Page earned an Academy Award nomination for Best Actress for the film.
In 1964, she starred in a Broadway revival of Anton Chekhov's Three Sisters playing eldest sister Olga to Kim Stanley's Masha with Shelley Winters as the interloper Natasha. BothShirley Knight and Sandy Dennis played the youngest sister Irina at different stages in this production. It was directed by Lee Strasberg (and a version of it was preserved on film). In 1967, Page starred in Peter Shaffer's Black Comedy/White Lies, a production which also included Michael Crawford and Lynn Redgrave who were making their Broadway debuts. Page received her second Tony nomination (for Best Featured Actress in a Play) for a successful production of Alan Ayckbourn's Absurd Person Singular with Sandy Dennis andRichard Kiley. Page also starred as Zelda Fitzgerald in the last major Broadway production of a Tennessee Williams play, Clothes for a Summer Hotel, which did not succeed financially on Broadway in 1980. In New York, she played Mary Todd Lincoln opposite Maya Angelou in a two-character play by Jerome Kilty called Look Away.
Page starred in another successful Broadway play, Agnes of God, which opened in 1982, and ran for 599 performances with Page performing in nearly all of them. She received a Tony Award nomination, for Best Lead Actress in a Play, for her performance as the secretive nun Mother Miriam Ruth.
After winning an Academy Award in 1986, Page returned to Broadway in a revival of Noël Coward's Blithe Spirit in the role of the psychic medium Madame Arcati. The production, which also starred Richard Chamberlain, Blythe Danner and Judith Ivey, was Page's last. Page was again nominated for a Tony Award, for Best Lead Actress in a Play. She did not win, and several days after the awards ceremony, she died. The show lasted several weeks more, with co-star actress Patricia Conolly taking over Page's role.
Her film debut was in Out of the Night (1947). Her role in Hondo, opposite John Wayne, garnered her a nomination for the Academy Award for Best Supporting Actress. In all, despite her relatively small filmography, Page received eight Academy Award nominations. She finally won the Oscar in 1986 for her performance in The Trip to Bountiful, which was based on a play by Horton Foote. When she won (F. Murray Abraham, upon opening the envelope, exclaimed, "I consider this woman the greatest actress in the English language"), she received a standing ovation from the audience. She was surprised by her win (she openly talked about being a seven-time Oscar loser), and took a while to get to the stage to accept the award because she had taken off her shoes while sitting in the audience. She had not expected to win, and her feet were sore.
Her other notable screen roles included Academy Award-nominated performances in Tennessee Williams' Summer and Smoke, Sweet Bird of Youth, You're a Big Boy Now, Pete 'n' Tillie, Woody Allen's Interiors and The Pope of Greenwich Village.
She also appeared in such roles as a psychotic serial killer in What Ever Happened to Aunt Alice?; a repressed schoolmistress in the Clint Eastwood film, The Beguiled; a charismatic evangelist (modeled after Aimee Semple McPherson) in The Day of the Locust; a nun, Sister Walburga, in Nasty Habits; and as 'Aunt' Beverly in Harry's War.
Her final film was the 1987 Mary Stuart Masterson film My Little Girl, which featured the film debut of Jennifer Lopez.
She performed in various television shows in the 1950s through the 1980s, including movies and series, such as Hawaii Five-O, Kojak, and several episodes of Rod Serling's Night Gallery, including "The Sins of the Fathers" and "Something in the Woodwork". She also was a voice actress and voiced the villainous Madame Medusa in the Disney animated filmThe Rescuers.
In 1959, Page was a Best Single Performance by an Actress Emmy nominee for her role on an episode of Playhouse 90. Page later received two Emmy Awards for her work in adaptations of Truman Capote stories. In 1967, she won an Emmy for Outstanding Single Performance by an Actress in a Leading Role in a Drama for her performance in A Christmas Memory on ABC Stage 67. In 1969, she received an Emmy for Outstanding Single Performance by an Actress in a Leading Role for her performance in The Thanksgiving Visitor.
Page, who suffered from kidney disease, died of a heart attack in 1987 during a run on Broadway in Sir Noël Coward's Blithe Spirit at the Neil Simon Theatre. She did not arrive for either of the show's two June 13 performances; at the end of the evening performance, the play's producer announced that she had died at the age of 62.
Five days after her death, "an overflow crowd of colleagues, friends and fans," including Sissy Spacek, James Earl Jones, Amanda Plummer and husband Rip Torn filled the Neil Simon Theatre to pay tribute. Her achievements as a stage actress and teacher were highlighted; actress Anne Jackson stated at the tribute that "[Page] used a stage like no one else I'd ever seen. It was like playing tennis with someone who had 26 arms." Torn called her "Mi corazon, mi alma, mi esposa" ("My heart, my soul, my wife") and said they, "Never stopped being lovers, and ... never will." Page was cremated.