After leading the TBJHL in points in 1942–43, Bodnar joined the Toronto Maple Leafs. On October 30, 1943, Bodnar scored his first ever NHL goal 15 seconds in his first NHL game, setting the record for fastest goal by a player in his first NHL game. Bodnar scored 62 points during the regular season, a career best, and he beat Montreal Canadiens rookie goaltender Bill Durnan in voting for the Calder Memorial Trophy in 1943–44. He spent four more seasons with the Maple Leafs and won two Stanley Cups in 1944–45 and 1946–47. Bodnar had 40 assists in his rookie season in 1943–44, which would set a record for assists by a Maple Leafs rookie until surpassed by Mitch Marner in 2016–17.