Dunne began his professional acting career at age 19 with a small supporting role in The Other Side of the Mountain in 1975. He has since appeared on both film and television, starring in An American Werewolf in London (1981) as Jack Goodman, Johnny Dangerously (1984) as Tommy Kelly, After Hours (1985) as Paul Hackett, Who's That Girl (1987) as Loudon Trott opposite Madonna, My Girl (1991) as Jake Bixler, Quiz Show (1994) as the Geritol Account Executive, Game 6 (2005) as Elliott Litvak and I Like It Like That (1994) as Stephen Price. Dunne also played Dr. Vass, opposite Matthew McConaughey, in the Oscar-nominated 2013 film Dallas Buyers Club.