Kozlov made his NHL debut on March 12, 1992, recording two assists in Detroit's 5–4 win over the St. Louis Blues.

After the Red Wings acquired Igor Larionov in 1995, coach Scotty Bowman created a 5–man Russian unit (the "Russian Five") consisting of forwards Kozlov, Sergei Fedorov and Igor Larionov, and defensemen Vladimir Konstantinov and Viacheslav Fetisov.

Kozlov played for Detroit until the summer of 2001, when he was traded to the Buffalo Sabres as part of a package for Dominik Hašek.

[citation needed] Kozlov re-signed with the Thrashers on July 4, 2007, signing a three-year, $11–million contract with a no-trade clause.

Kozlov played his 1,000th NHL game on December 26, 2007, against the Columbus Blue Jackets and his former Russian Five teammate, Sergei Fedorov.

Ufa's star-studded team advanced to the KHL finals and captured the Gagarin Cup, beating Atlant Moscow Oblast 4 games to 1.

On 11 October 2020, Vladislav signed a two-year, $4 million contract with the Detroit Red Wings, Kozlov's former team.