Saprykin spent the entire 2003–04 season in Calgary and recorded 29 points in 69 games. He then played with the team in the 2004 Stanley Cup Playoffs as the Flames, who had missed the post-season the previous seven seasons, went on a Cinderella run to the Stanley Cup Final. Saprykin recorded six points in 26 games during the run; of his three goals, none was larger than his overtime winning goal in game five of the final, against the Tampa Bay Lightning. Standing in front of the net, Saprykin collected the puck on a rebound following a Jarome Iginla shot and scored to bring the Flames within one win of capturing the Stanley Cup. The Flames were unable to win the title, as they lost both the sixth and deciding seventh games of the series.