The Black Hawks traded Crozier to the Detroit Red Wings in 1963. The young goaltender, now a full-time professional, spent the season in the minors mostly with the St. Louis Braves in the EPHL; he also played four games for the Buffalo Bisons in the AHL. In 1963–64, he played 44 games with the Pittsburgh Hornets, Detroit's AHL affiliate. He won numerous awards that year, including the Hap Holmes Memorial Award for the fewest goals given up, the Dudley "Red" Garrett Memorial Award for top rookie, and a spot on the Second All-Star Team. Crozier also made his NHL debut that season. The Red Wings' starting goaltender, Terry Sawchuk, was injured and Crozier was called up as a substitute. In only 15 games, he impressed management so well that he was made the Wings' new starting goaltender.; Sawchuk was left unprotected by the Red Wings during the intraleague waiver draft in the off-season and was picked up by the Toronto Maple Leafs. This made Crozier the Red Wings' starting goaltender at the age of 22.