When Stephenson first stepped onto the scene, he was playing for the Winnipeg Braves in the Manitoba Junior League starting in the 1963-64, going 11-15-3 in 29 games. Returning to the Braves in the 1964-65 season, Stephenson would go 26-12-5 in 43 games, then 4-0 in four playoff games, helping win the league championship.After the season, Stephenson was MJHL MVP, top goalie, and on the first-team all-star squad. Stephenson was picked by the Edmonton Oil Kings to participate in the 1965 Memorial Cup, where he would go 1-4 in five games
Post-junior career, Stephenson chose to join the Canadian National team under the tutelage of Father David Bauer. Stephenson played with the Canadian National team from the 1966-67 season until the 1970-71 season. In that time, Stephenson played in two World Championships (1967, 1969) and one Olympics in 1968, where he would go 2-0-0 in three appearances, helping the Canadians win a Bronze medal. Stephenson also played 15 games for the Winnipeg Nationals in the 1967-68 in the Western Canada Senior League.
For the 1971-72 season, Stephenson would get signed on in January with the St. Louis Blues and spend most of the season in the Central League with the Kansas City Blues, going 5-11-4 in 21 games; then going 0-1-0 in two games with St. Louis. Stephenson spent the entire 1972-73 season with St. Louis, playing in 45 games and finishing with a 18-15-7 record, then going 1-2 in three playoff games. Returning to St. Louis in 1973-74 season, Stephenson went 13-21-5 in 40 games.
Before the 1974-75 season, Stephenson was traded to the Philadelphia Flyers, where he would be behind Bernie Parent on the depth chart; playing only 12 games and going 7-2-1, then 2-0 in two playoff games, helping the Flyers win the Stanley Cup. In the 1975-76 season, Stephenson got most of the games in for the Flyers, as Parent was injured-- going 40-10-13 in 66 games, then 4-4 in eight playoff games. With Parent back in 1976-77, Stephenson was resigned to the bench again, playing in only 21 games, going 12-3-2 and 4-3 in nine playoff games. Stephenson got more games in during the 1977-78 season, playing in 26 games and finished with a 14-10-1 record. During the 1978-79 season, Parent suffered a career-ending eye injury, resulting in Stephenson seeing more time, compiling a 20-10-5 record in 40 games, then 0-3 in four playoff games that season.
During the summer of 1979, Stephenson was traded to the Washington Capitals, where he would play 56 games in the 1979-80 season, posting an 18-24-10 record. For the 1980-81 season, Stephenson would be back to the Capitals, playing only 20 games with a 4-7-5 record, which would lead to his retirement after the season.
Post playing career, Stephenson got into the financial industry, working banks in Philadelphia, Milwaukee, and Cape Cod. However, he would be diagnosed with terminal brain cancer and would pass away on August 22, 2010.
Though he didn't have one of the most straight tracks to the NHL, he was able to get to the show and succeed as much as he could in his short time there. He had a great team in front of him, which helped showed off what he could do with the right team in front of him.