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 Lou Rothkopf and Leo Berkowitz, primarily between Cleveland, Ohio and 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/Mayfield Road area, such as John "King" Angersola, Alfred Polizzi and the Milano brothers 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.
Dalitz continued to be active in the Las Vegas community. In 1982 he received the Torch of Liberty Award by the Anti-Defamation League of B'nai B'rith. When he died in 1989 many organizations received substantial donations he left in his will.