After playing just over two full seasons with his hometown junior Winnipeg Monarchs (1960-62), Stemkowski transferred to the Toronto Marlboros. He helped them win the Memorial Cup in 1963-64. He turned pro the next season, but the Toronto Maple Leafs coach Punch Imlach was not a fan of young players. Stemkowski split the next two seasons between the Leafs and their farm team Rochester Americans. He became a full time Leaf in 1966-67 and helped thyem win the Stanley Cup that year. Since then, Stemkowski has done media work in hockey.