Born in Brooklyn, New York, Rosenstein played at City College of New York and was a member of the original roster New York Knickerbockers, playing with them in what is now cosnsidered the first NBA game, played in Toronto on November 1, 1946, and in their first season, 1946/1947. Prior to joining the Knicks, Hank starred in AAU Basketball and was MVP in the Eastern Jewish Center League in 1942–43.
After the Knicks, Rosenstein played for five seasons with the Scranton Miners of the American Basketball League, playing on their championship teams in 1949–50 and 1950–51. In the latter year he led the team in scoring.
- Vincent M. Mallozzi, "Hank Rosenstein, Player in First N.B.A. Game, Dies at 89", New York Times, March 3, 2010; page A27.