Crozier coached Buffalo for three seasons after taking over for Punch Imlach, who stepped down due to health concerns, in January 1972. He is credited with putting together its famed "French Connection" line of Gilbert Perreault, Rick Martin and Rene Robert.
In 1972-73, his second season and the Sabres' third as a franchise, they went 37-27 with 14 ties and qualified for the playoffs for the first time, losing in the quarterfinals to the Montreal Canadiens in six games.
After Buffalo missed the playoffs the following season, Crozier was replaced by Floyd Smith. He finished with a record of 77-80 with 35 ties.
Crozier spent the following three seasons as coach of Vancouver and Calgary in the World Hockey Association before ultimately returning to the NHL with the Toronto Maple Leafs in 1980-81. However, after starting the season 13-22 with five ties, he was replaced by Mike Nykoluk. He returned behind the Buffalo bench as an assistant in 1984-85.
As a player, Crozier had three assists in five NHL games as a defenseman for the Maple Leafs in 1959-60.
Prior to becoming an NHL coach, Crozier coached Rochester of the American Hockey League to three Calder Cup championships in four seasons (1965, 1966 and 1968) and Vancouver to a Western Hockey League championship in 1969. He later guided Kitchener of the Ontario Hockey League to a Memorial Cup championship in 1982 while coaching future Hockey Hall of Fame defensemen Scott Stevens and Al MacInnis.
After retiring from coaching, Crozier worked in the Sabres front office and was inducted into their Hall of Fame in 2010. He was also induced into the AHL Hall of Fame in 2012.
