In 1964–65, his rookie season, Crozier started all of his team's games, the last goalie to do so in the NHL, and he led the league in wins and shutouts with 40 and six respectively. His 2.42 GAA was the second lowest in the league. He was awarded the Calder Memorial Trophy as the NHL's top rookie and he was named to the NHL First All-Star Team. During his sophomore season, Crozier missed the team's couple of games due to pancreatitis. In 64 games that year, he posted 27 wins and led the league with seven shutouts, and the Red Wings clinched a spot in the playoffs. After eliminating the Black Hawks in the semi-finals, the Red Wings squared off against the Montreal Canadiens in the 1966 Stanley Cup Finals. The Red Wings won the first two games, but the Canadiens came back and won the next two. In the fourth game, Crozier suffered a leg injury. He played in game five, but the injury curbed his mobility. The Canadiens won the Stanley Cup in game six. Even though the Red Wings lost, Crozier was awarded the Conn Smythe Trophy for being the most valuable player in the playoffs. He was the first goaltender to win the award and the first player to win it in a losing effort.