In 1983, Quinn lost the role of Jesus Christ when Paramount Pictures dropped the distribution rights to the Martin Scorsese movie The Last Temptation of Christ. When Universal Pictures picked up the film, the role went to Willem Dafoe. In the meantime, Quinn starred as protagonist in the film Crusoe, finished in 1989.
His first significant film role was in Reckless, followed by a breakthrough role in Desperately Seeking Susan as the character "Dez" (the love interest of the character played by Rosanna Arquette). Quinn next starred in the controversial television film An Early Frost, about a young gay Lawyer dying of AIDS (it was broadcast on NBC on November 11, 1985, and co-starred Gena Rowlands, Ben Gazzara and Sylvia Sidney). He received his first Emmy Award nomination for the role which allowed him to gain recognition in Hollywood. He made a short impressive contribution as Robert De Niro's brother in The Mission. He played escaped convict Richard "Stick" Montgomery in the action comedy Stakeout opposite Richard Dreyfuss and Emilio Estevez.
In 1987, Quinn married his Stakeout co-star, Elizabeth Bracco (sister of Actress Lorraine Bracco). They have two daughters: Mia (b. 1998) and Ava Eileen (b. 1989) , who has autism. Ava appeared as the baby "David" in Avalon, and Mia played a ghost in The Eclipse. Former residents of Englewood, New Jersey, Quinn and his family now live in Palisades, Rockland County, New York and Marbletown in the Catskills / Woodstock region of Ulster County, New York.
During the 1990s, he appeared in Legends of the Fall, Benny & Joon, The Handmaid's Tale, Haunted and Practical Magic. He also starred in Michael Collins, Song for a Raggy Boy, This Is My Father, and Evelyn. He played a small cameo as the captain of a doomed Arctic vessel in the Francis Ford Coppola-produced adaptation of Frankenstein.
In 2000, Quinn portrayed Paul McCartney in the VH1 television drama, Two of Us.
Quinn spoke at the 2003 "Night of Too Many Stars" gala benefiting The Autism Coalition. He was an honorary board member of the National Alliance for Autism Research (NAAR), which merged with Autism Speaks.
Quinn appeared in the 2005 movie The Exonerated a true story about people on death row who had been freed in which Quinn played Kerry Max Cook.
Quinn played the main character on the NBC drama The Book of Daniel, in 2006. The show was canceled after the first three weeks of its run, and its last five episodes never aired. In 2007, Quinn received his second Emmy nomination for the television movie Bury My Heart at Wounded Knee.
Quinn has participated in charity golf events for the East Lake Foundation, a community redevelopment program, and Samuel L. Jackson's "One for the Boys" campaign about testicular cancer awareness. In 2010, Quinn attended a premiere benefit screening of A Shine of Rainbows for the International Children's Media Center (ICMC) and The American Ireland Fund (AIF). In 1991, he read a segment from Franz Kafka's The Metamorphosis as part of MTV's "Books: Feed Your Head" literacy promotion PSAs.
He starred as "Dermot" opposite Taylor Schilling (Abby) in the Canadian-Irish drama film Stay (2013).