After the 1995 draft, Kuznetsov played for the Dynamo Moscow before making the trip to North America.
Unfortunately, a knee injury suffered in a game against Vancouver caused him to miss much of the remaining season.
In the latter part of the 02–03 season, Kuznetsov was traded to the Los Angeles Kings along with Sean Avery and two draft picks for Mathieu Schneider.
Upon his arrival with the Kings organization, he spent the majority of his playing time with the team's AHL affiliate, the Manchester Monarchs.
On June 7, 2004 Kuznetsov signed as a free agent with Dynamo Moscow (due to the NHL lockout) once again.