Torgayev spent 12 seasons in the Soviet League before moving to Finland for two years in 1993. After being drafted by the Flames, Torgayev came to North America, where he appeared in 41 regular season games with the Flames in 1995–96, recording six goals and ten assists in 41 games. After returning to Europe to play in Switzerland for three seasons, Torgayev once again returned to the NHL in 1999–00, Torgayev appeared in nine more games with the Flames before being claimed by Tampa Bay on waivers. After playing five more games with the Lightning, he refused an assignment to the minor leagues, and returned to Russia, where he remained until his retirement following the 2004–05 season.