25 goals to lead the Predators, finished 3rd on the club with 48 points, and was selected to be the franchise's representative at the 1999 NHL All-Star Game. His season was topped by the opportunity to represent Russia at the 1998 Winter Olympics, where he helped his country to a silver medal. Unfortunately, his success in Nashville would be short-lived. In 1999–2000, the inconsistency he showed in Chicago returned and he was replaced on the team's top line by Patric Kjellberg. Krivokrasov is credited with scoring the first NHL goal of the 21st century, in a 3-2 win against the San Jose Sharks on January 1, 2000. With just 9 goals and 26 points through 63 games, he was dealt at the NHL trade deadline to the Calgary Flames for Cale Hulse and a 3rd round draft pick. In Calgary, he responded well with 1 goal and 10 assists in 12 games to finish the year with 10 goals and 27 assists (a career high) for 37 points. However, Calgary decided to expose him in the 2000 NHL Expansion Draft where he was claimed by the Minnesota Wild. Minnesota hoped that Krivokrasov could duplicate his performance two seasons prior for the first-year Predators, but he never settled into the defense-first system of head coach Jacques Lemaire. He finished the 2000–01 season with totals of just 7 goals and 22 points in 54 games, his lowest totals since 1996. 9 games into the 2001–02 campaign, he was dealt to the Mighty Ducks of Anaheim for a 7th round draft pick. In Anaheim, he fared no better, scoring just 1 goal in 17 games before being assigned to the minors for the first time in six years. With his NHL career at a standstill, Krivokrasov returned to Russia for the 2002-03 season, signing for Amur Khabarovsk. He would have a fine season, finishing with 16 goals and 18 assists in 51 games. Towards the end of the 2003-04 season, he was moved to Avangard Omsk, one of the top teams in the Russian Hockey League, where he helped the team to the 2004 championship. This was not without controversy, however, as he was a central player in the Krivokrasov stick incident in the semifinals, after exchanging an illegal stick during a delay prior to measurement. Krivokrasov's final few seasons in the Russian league would be nomadic as he appeared for 5 clubs