Bennett was born Michael Bennett DiFiglia in Buffalo, New York, the son of Helen (nee Ternoff), a secretary, and Salvatore Joseph DiFiglia, a factory worker. His father was Roman Catholic and Italian American and his mother was Jewish. He studied dance and choreography in his teens and staged a number of shows in his local high school before dropping out to accept the role of Baby John in the US and European tours of West Side Story.  Bennett's career as a Broadway dancer began in the 1961 Betty Comden-Adolph Green-Jule Styne musical Subways Are for Sleeping, after which he appeared in Meredith Willson's Here's Love and the short-lived Bajour. In the mid-1960s he was a featured dancer on the NBC pop music series Hullabaloo, where he met fellow dancer Donna McKechnie.  Bennett made his choreographic debut with A Joyful Noise (1966), which lasted only twelve performances, and in 1967 followed it with another failure, Henry, Sweet Henry (based on the Peter Sellers film The World of Henry Orient). Success finally arrived in 1968, when he choreographed the hit musical Promises, Promises on Broadway. With a contemporary pop score by Burt Bacharach and Hal David, a wisecracking book by Neil Simon and Bennett's well-received production numbers, including "Turkey Lurkey Time", the show ran for 1,281 performances. Over the next few years, he earned praise for his work on the straight play Twigs with Sada Thompson and the musical Coco with Katharine Hepburn. These were followed by two Stephen Sondheim productions, Company and Follies co-directed with Hal Prince.  In 1973, Bennett was asked by producers Joseph Kipness and Larry Kasha to take over the ailing Cy Coleman-Dorothy Fields musical Seesaw. In replacing the director Ed Sherin and choreographer Grover Dale, he asked for absolute control over the production as director and choreographer and received credit as "having written, directed, and choreographed" the show.

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