Winn was born in Washington, D.C. She spent much of her childhood time traveling to China, India and Japan.

She was in the American Conservatory Theater's first production of Tartuffe in 1967.

She made her Broadway debut in 1969 in The Three Sisters, and won Best Actress at the 1971 Cannes Film Festival for her role opposite Al Pacino in The Panic in Needle Park. She also starred in New York's Shakespeare in the Park production of Hamlet.

Winn is perhaps best known for her role as Sharon in the Academy Award winning motion picture The Exorcist, and again in Exorcist II: The Heretic.

Her last film was Mirrors in 1978, in which she took the lead role of Marriane.

In the late 1970s, she was an Artist-in-Residence at the University of North Carolina at Greensboro.