Baker was born and raised in Hollywood, California. She is the daughter of Dorothy Helen Harrington, who had appeared in several early Marx Brothers movies, and Clyde L. Baker. Baker has two younger sisters, Patti and Sheri. At age 18, Baker moved to New York to study acting with Charles Conrad and ballet with Nina Fonaroff.
After securing a contract with 20th Century Fox, Baker made her film debut when she was chosen by director George Stevens to play Margot Frank in the 1959 motion picture The Diary of Anne Frank. In the same year, she starred in Journey to the Center of the Earth with James Mason and in The Best of Everything with Hope Lange and Joan Crawford.
Other Fox films in which Baker appeared include the assassination thriller Nine Hours to Rama, Hemingway's Adventures of a Young Man and The 300 Spartans. Her television work in the late 1950s and 1960s includes appearances on Follow the Sun, Bus Stop, Adventures in Paradise, The Lloyd Bridges Show, The Nurses, The Invaders (in the first episode), and Route 66.
Finally out of her contract with Fox after starring in 1960 in the fourth screen version of Grace Miller White's novel Tess of the Storm Country, Baker appeared in The 300 Spartans (1962) and Stolen Hours, a 1963 remake of Dark Victory, and, the same year, opposite Paul Newman and Elke Sommer in The Prize. From 1963 to 1966, Baker had a recurring role on the medical drama Dr. Kildare.
In 1964, she co-starred with Joan Crawford in both Strait-Jacket, the William Castle-directed thriller about an axe murderess, and an unsold television pilot Royal Bay, released to theaters as Della. Alfred Hitchcock cast her in his film Marnie (1964) as Lil Mainwaring, the sister-in-law of Mark Rutland (Sean Connery). She co-starred with Gregory Peck and Walter Matthau in the thriller Mirage (1965), directed by Edward Dmytryk, and in Krakatoa, East of Java (1969) with Maximilian Schell. In the TV movie Western The Dangerous Days of Kiowa Jones (1966), she played the role of a woman who falls in love with a drifter (Robert Horton) who is deputized by a dying marshal to take two killers (one of whom is played by Sal Mineo) to a distant jail.
In August 1967, Baker had the distinction of playing David Janssen's love interest in the two-part finale of The Fugitive, which became the most-watched show in the history of episodic television up until that time. In 1968, she co-starred with Dean Jones in the Disney film The Horse in the Gray Flannel Suit. In January 1970, she had the lead guest-starring female role as Princess Francesca in the only three-episode mission of Mission: Impossible. In 1973, Baker co-starred in ABC sitcom Here We Go Again. The series was canceled after one season. In 1976, she played the alcoholic daughter of the title character of the Columbo episode "Last Salute to the Commodore".
In the decades after Mirage, she appeared frequently on television and began producing films, including the drama film Never Never Land (1980) and the miniseries A Woman of Substance (1984), in which she played Laura. She reemerged on the big screen in The Silence of the Lambs (1991) as Senator Ruth Martin ("Love your suit," Hannibal Lecter memorably said to her). Baker also appeared in the films The Joy Luck Club, The Cable Guy, The Net and A Mighty Wind. She guest starred in four episodes of House in 2005, 2008 and twice in 2012 as Blythe House, the mother of the title character.
Since August 2004, Baker has been the director of the Motion Pictures and Television major at Academy of Art University in San Francisco.