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. He was also one of the top players on the Russian squad which won the 1992 World Junior Championships. Impressed with his grit and goalscoring ability, the Chicago Blackhawks selected him in the first round, 12th overall, in the 1992 NHL Entry Draft. Krivokrasov quickly signed with Chicago and was assigned to the Indianapolis Ice, the team's IHL affiliate for the 1992–93 season, where he impressed with 36 goals and 69 points as a rookie, and earned a four-game callup to Chicago. He remained in Indianapolis in 1993–94, and although his production dropped at that level he appeared in another 9 games for Chicago, scoring his first NHL goal. During the 1994–95 NHL lockout Krivokrasov was again in Indianapolis, but he was quickly promoted to Chicago at the conclusion of the lockout in January, and played regularly for Chicago for the rest of the campaign. His rookie season was an excellent one, as he posted 12 goals and 7 assists for 19 points in 41 games. His 12 goals placed him 6th on the Hawks and 8th amongst all NHL rookies. However, after the success of his rookie year, the rest of Krivokrasov's stay in Chicago would be unsettled. He was briefly reassigned to Indianapolis in the midst of a disappointing sophomore campaign that saw him score only 6 goals in 46 games. 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. In 1996-97, he set career highs with 13 goals and 24 points, but his offensive production was still below what was expected given his promising start. After scoring only 10 goals in 1997–98, he was dealt to the expansion Nashville Predators in the summer of 1998. 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. 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. 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 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 coachJacques 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 between 2004 and 2008, most notably a return to his first club CSKA Moscow in 2005–06. After two seasons with Metallurg Novokuznetsk, he retired in 2008. He now lives in Denver, CO. Krivokrasov finished his career with totals of 86 goals and 109 assists for 195 points in 450 NHL games. In the various incarnations of the top Russian division, he added an additional 93 goals and 82 assists for 175 points in 375 games.