Dinnerstein was of Jewish descent, with ancestors from Austria, Romania, and what became Belarus.
He attended Theodore Roosevelt High School, and graduated from the City College of New York before pursuing further study in American history at Columbia University.
After completing his doctorate, Dinnerstein taught at New York Institute of Technology and Fairleigh Dickinson University.
He then joined the University of Arizona faculty as professor from 1970 to 2004.
Dinnerstein died of complications from kidney failure in Tucson, Arizona on January 22, 2019, aged 84.