Born to bellhop Eugene Pleshette and dancer Gloria Kaplan, she is a cousin of Knots Landing actor John Pleshette.

Pleshette has been in over two dozen made-for-television films and numerous film dramas of the late '50s, '60s and '70s. She has been nominated for an Emmy Award several times, most notably for Dr. Kildare.

Pleshette is a former Broadway leading lady, having replaced Anne Bancroft in The Miracle Worker opposite Patty Duke to rave reviews. She also provided the voices of Yubaba and Zeniba in the English dub of Japanese director Hayao Miyazaki's Academy Award winning film Spirited Away. Perhaps the most memorable of her film roles was that of Annie in the Hitchcock classic The Birds.

She appeared in the ABC sitcom 8 Simple Rules after John Ritter's death in September 2003; she played the mother of Katey Sagal's character. She has also guest-starred in several episodes of the NBC sitcom Will & Grace as the estranged mother of Megan Mullally's character Karen Walker.

Pleshette's first marriage was in 1964, to Rome Adventure co-star Troy Donahue; they divorced acrimoniously eight months later. She married Thomas Gallagher in 1968 and they remained married until his death from cancer on January 21, 2000. She has never had children. In 2001, Suzanne married a former co-star, comic actor Tom Poston (born 1921) who played "The Peeper", a college friend of Bob Hartley on The Bob Newhart Show (as well as the handyman on Newhart).