Born in Boston, Massachusetts and raised in Michigan, Dalitz worked in his family's laundry business early on, but began his career in bootlegging when Prohibition began in 1919, and capitalized on his access to the laundry trucks in the family business. He ran a leading rumrunning group called the "Little Jewish Navy" with partners Louis "Lou Roddy" Rothkopf, and adopted member of the Polizzi family, Leo "Charles Polizzi" Berkowitz, all of whom operated primarily between Cleveland, Ohio, Detroit and Ann Arbor, Michigan during the Prohibition era. Moe Dalitz formed strong ties within Cleveland's Eastside, Little Italy community. He later merged his group with top underworld leaders from the Murray Hill and Mayfield Road area, such as brothers Fred "Freddy King" and John "Johnny King" Angersola, Alfred "The Owl" Polizzi and brothers Anthony and Frank Milano of the "Mayfield Road Mob" to form the leading underworld organization in Cleveland. While converting his profits into legitimate businesses, he also owned several illegal casinos in Cleveland.
His investments in Las Vegas began in the late 1940s with the Desert Inn when the original builder of the resort, Wilbur Clark, ran out of money, and Dalitz took over the construction. When it opened in 1950, Clark remained the public face and frontman of the resort, while Dalitz quietly remained in the background as the real owner. He also ran the Stardust Resort & Casino for a time after the death of Tony Cornero. Dalitz owned the Desert Inn until 1967, when he sold it to the billionaire Howard Hughes. Since he had been under constant pressure from law enforcement for many years, selling the resort was seen as an opportunity to get the authorities off his back. Dalitz had ties to both Jimmy Hoffa and Lew Wasserman of MCA, both of whom were subject to extensive criminal and anti-trust investigations in the 1960's. Hoffa had testified to his longtime relationship with Dalitz through union representation of his dry cleaners. Wasserman had first worked at a Cleveland club owned by Dalitz and his associates.
Moe Dalitz was also a longtime friend of Meyer Lansky, one of the main architects of modern organized crime. To the FBI, Dalitz played a vital role inside Lansky's powerful organization which also included men like Louis Chesler, The Cellini brothers, Vincent "Jimmy Blue Eyes" Alo, Harry "Nig Rosen" Stromberg and actor, George Raft. In 1982, Dalitz received the "Torch of Liberty" award from the Anti-Defamation League.
In the 1970's Dalitz filed a massive defamation suit against Penthouse magazine over an article written by Lowell Bergman about Rancho La Costa, a resort funded by the Teamsters. Dalitz continued to be active in the Las Vegas community. When he died in 1989 many organizations received substantial donations he left in his will.