A member of Chicago's Goodman and Steppenwolf Theatre acting companies, Quinn made his film debut as a rebellious youth in 1984's Reckless. The next year, he starred opposite Madonna in Desperately Seeking Susan and in the first AIDS-themed telefilm, An Early Frost (for which he earned his first Emmy nod). He became increasingly visible in such films as Stakeout and The Mission and Crusoe.
Since the 1990s, Quinn has alternated between feature films (such as Mary Shelley's Frankenstein, Legends of the Fall and Music of the Heart) and numerous roles in works for television, including 2007's Bury My Heart at Wounded Knee, the critically acclaimed made-for-TV movie that garnered him another Emmy nod.