Born in Trail, British Columbia, Zanier's junior career was spent with five different teams in the WHL. He was never drafted, but signed with the Edmonton Oilers where he saw some NHL playing time. Zanier dressed for games 4 and 5 of the 1984 Stanley Cup Finals, due to Grant Fuhr being injured. He did not appear in either game. Although the Oilers won the Cup, Zanier's name was not engraved on it because he had not officially played in any NHL games. However, he did receive a Stanley Cup ring. Zanier did play three games for Edmonton during the next season, but that was the extent of his NHL career. Zanier went on to play many seasons in Europe, and represented Italy at the 1992 Winter Olympics.