After two seasons in the WHL with the Seattle Thunderbirds, Turner Stevenson was selected 12th overall by the Canadiens in the 1990 NHL Entry Draft. He played in the World Junior Championships for team Canada in 1992 and was named to the WHL's First All-Star team and Memorial Cup All-Star team. Stevenson made his NHL debut playing one game during the 1992-93 season, but he spent the rest of the year with the team's AHL affiliate in Fredericton. After two more seasons in the minors, Stevenson split time with Fredericton and Montreal in 1994-95. He stayed up for good in 1995-96 and played the next four seasons in Montreal before being claimed by the Columbus Blue Jackets in the Expansion Draft of 2000.
Columbus dealt Stevenson to the New Jersey Devils before he had a chance to play a game with the expansion team. As a checking forward, Stevenson helped the Devils reach the Stanley Cup finals where they took Colorado to a seventh game before succumbing. After an injury plagued 2001-02 season, the bruising winger returned the following year and was an instrumental player in New Jersey's successful playoff run and their 2003 Stanley Cup win. Stevenson went on to play four seasons with the Devils before signing as a free-agent with the Philadelphia Flyers in the summer of 2004.