Born in Peoria, Illinois, Irwin graduated from Illinois State University in Normal, Illinois. He joined the Steppenwolf Theatre Company in 1979, where he performed alongside Laurie Metcalf, John Malkovich, Joan Allen, and Gary Sinise. Irwin has been on the faculty of The Goodman School of Drama at DePaul University and Columbia College in Chicago. He is a class instructor at Steppenwolf Theater West School of Drama in Los Angeles, California. He has appeared in over thirty Steppenwolf productions, and won a Joseph Jefferson Award for his performance as Tom in Steppenwolf's The Glass Menagerie.
His first starring television role was in 1991, in the short-lived ABC television series, My Life and Times. He starred as Graham Chase, the soft-spoken father in the 1994 ABC television series My So-Called Life. He has had numerous other television acting appearances, including Angel, ER, and Lost. He had a regular role on the television series Saving Grace for three seasons, beginning in 2007. He made his Broadway debut in 1990 in The Grapes of Wrath. Irwin, who has also appeared in various movie roles, lives in Los Angeles, California. In 2002 he played the part of Gerry in London's West End production of Up for Grabs with Madonna. In 1999, he starred in No Higher Love, with Katey Sagal and Annabeth Gish, about a woman with a terminal illness who chooses someone to take over for her as wife and mother. As of 2013, Irwin starring opposite Rebecca Wisocky in the Lifetime television comedy-drama series Devious Maids.