Born in the Bronx, Reilly studied with Uta Hagen alongside fellow students Steve McQueen, Geraldine Page and Hal Holbrook. He made his Broadway debut in Bye Bye Birdie and won a Best Featured Actor Tony Award in 1962 for creating the role of Bud Frump in How to Succeed in Business Without Really Trying. Two years later, he was nominated for another Featured Actor Tony for playing Cornelius Hackl in Hello, Dolly!. Other Broadway appearences as an actor included the short-lived shows Skyscraper, God's Favorite and Charlotte.
TV viewers knew Reilly from his regular appearances on the game shows Hollywood Squares and Match Game in the 1970s and '80s, where his often risque one-liners and distinctive laugh made him an audience favorite. He appeared as a guest on the Johnny Carson-era Tonight Show almost 100 times, and was a frequent guest on The Dean Martin Show. Reilly received Emmy Award nominations for his supporting role in the 1960 series The Ghost and Mrs. Muir and for his guest appearences on The Drew Carey Show and Millennium.
His final work was an autobiographical one-man show, Save It for the Stage: The Life of Reilly, about his family life growing up in the Bronx. The stage show was made into a 2006 feature film called The Life of Reilly. Reilly is survived by his partner, Patrick Hughes.