A roofer by trade, Quinn made a splash in his professional stage debut, a Chicago production of "The Man in 605", and later Off-Broadway in Sam Shepard's "Fool for Love" (1983). He launched his motion picture career as motorcycle-riding rebel Johnny Rourke in James Foley's "Reckless" (1984) and followed up with his portrayal of a bohemian projectionist in "Desperately Seeking Susan" and an acclaimed performance in "An Early Frost" (NBC, 1985), the first TV-movie to address AIDS. Quinn's inherently sympathetic quality helped make the story more palatable to middle-American sensibilities and earned him an Emmy nomination. He made a short, impressive contribution to "The Mission" (1996) and then starred in the PBS "Great Performances" production of Arthur Miller's "All My Sons" (1987). As for theater, he acted Off-Broadway in Shepard's "A Lie of the Mind", made his stage directing debut the following year at NYC's Ensemble Studio Theatre's "Marathon '86" and scored a modest success following in Marlon Brando's stead as Stanley Kowalski in the Broadway revival of Tennessee Williams' "A Streetcar Named Desire" (1988).

Quinn followed his villainous turn in John Badham's "Stakeout" (1987) with a starring performance in "Crusoe" (1988), a revisionist adaptation of Daniel Defoe's oft-filmed 1719 novel "Robinson Crusoe" which, though beautifully photographed, amounted to too little story for too much screen time. He portrayed Nick, the driver of Robert Duvall and lover of Natasha Richardson, in the well-mounted but ultimately sterile sci-fi offering "The Handmaid's Tale" (1989) and played a character based on Barry Levinson's father in the director's third feature set in his native Baltimore, "Avalon" (1990). As the traveling Irish player in "The Playboys" (1992), he added more spice to an already dicey mix, but his role as the brother of a mentally disturbed Mary Stuart Masterson cast him rather thanklessly as the reality base and opponent of love in "Benny & Joon" (1993), a movie which scored more points for the quirky romance between Masterson and Johnny Depp. In the same year as "Legends of the Fall", he also appeared as the bearded ship's captain who listens to Dr. Frankenstein's tragic tale in "Mary Shelley's Frankenstein" (1994).

Quinn reteamed with Duvall for James Keach's "The Stars Fell on Henrietta" (1995), playing a young farmer whose land may sit atop an oil reserve in the Depression-era Texas Dust Bowl. He appeared as Richmond in Al Pacino's ingenious documentary exploration of Shakespeare, "Looking for Richard", and was winning as Harry Boland, co-strategist and romantic rival of "Michael Collins" (both 1996), Neil Jordan's epic take on the Irish freedom fighter. Canadian director Christian Duguay gave him his second opportunity to play a dual role in "The Assignment" (1997), an intelligent, gripping thriller which cast him not only as Carlos the Jackal but also as the "dead ringer" Navy man trained to impersonate and thereby undermine the terrorist. (He had portrayed twins in the USA movie "Lies of the Twins" 1991). Quinn also portrayed Henry Morton Stanley in "Forbidden Territory: Stanley's Search for Livingston" (ABC, 1997), adding Kenya to his list of exotic locations including Latin American jungles for both "The Mission" and "At Play in the Fields of the Lord" (1991) and the extremely primitive Seychelles island group for "Crusoe". He returned to his beloved Ireland for "This Is My Father" (1998), a family affair written and directed by his brother Paul and shot by his brother Declan. Appearing in flashbacks, he deftly played the adopted son of poor farmers whose romance with a spirited underage girl could only result in tragedy.