Krivokrasov came up through the ranks of the famed CSKA Moscow club in Russia, breaking into the full squad at age 17 in 1991–92 and scoring 10 goals.

Impressed with his grit and goalscoring ability, the Chicago Blackhawks selected him in the first round, 12th overall, in the 1992 NHL Entry Draft.

He did, however, score the biggest goal of his NHL career, an overtime winner against the Colorado Avalanche in Game 4 of their second round playoff series.

On a first-year expansion team in Nashville, Krivokrasov was given more responsibility than he'd received in Chicago, and responded with the finest season of his career.

He nearly doubled his career high with 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.

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.

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.