Saprykin spent the 2000–01 season with the Flames. He scored his first NHL goal on October 24, 2000, against goaltender Sean Burke of the Phoenix Coyotes. He finished the year with nine goals and 23 points in 59 games. The Flames assigned Saprykin to their American Hockey League (AHL) affiliate, the Saint John Flames for the majority of the 2001–02 season; He played only three games in Calgary but had 24 points in 52 AHL games. He was again assigned to Saint John to begin the 2002–03 season but put his career in jeopardy by failing to report to the team. The Flames suspended Saprykin, but he rejoined his team four days later, and by the start of December had been recalled to Calgary. He finished the season with 21 points in 21 games with Saint John, and 23 points in 52 games in Calgary. Saprykin then made his debut with the Russian National Team; He scored one goal and three assists in seven games for the seventh place Russians at the 2003 World Championship.