Born in the Bronx on January 13, 1931, Reilly first gained fame in 1962, playing the role of the conniving Bud Frump in the musical How to Succeed in Business Without Really Trying. He won a Tony Award for his performance, and subsequently received a Tony nomination for his role of Cornelius Hackl in the original production of Hello, Dolly! His other Broadway credits as an actor included Bye, Bye Birdie (understudying Dick Van Dyke in the role of Albert Peterson), the musical Skyscraper, and the Neil Simon comedy God's Favorite.
Reilly had a second career as a Broadway director. He received a Tony nomination for the 1997 revival of The Gin Game, which starred Julie Harris and Charles Durning. He also directed The Belle of Amherst (another Julie Harris vehicle), Paul Robeson, Break a Leg, and The Nerd.
After first making his mark on Broadway in the 1960s, Reilly moved to Hollywood and landed the role of the nervous Claymore Gregg in the TV series The Ghost and Mrs. Muir. He was a frequent guest on The Dean Martin Show and became a television fixture with his appearances on The Hollywood Squares and The Match Game. In addition, he appeared on The Tonight Show with Johnny Carson nearly 100 times.
More recently, he toured in a one-man show titled Save it for the Stage: The Life of Reilly, in which he told hilarious and touching stories of his journey from his formative years in the Bronx to his successes in the theater and television. A feature film based on the show was released in 2006. Reailly also may be seen and heard as one of the "talking heads" in Rick McKay's documentary film Broadway: The Golden Age, passionately discoursing on the glories of live theater.
Reilly is survived by his longtime partner, Patrick Hughes.