He played in the National Hockey League with the Quebec Nordiques, Colorado Avalanche, Montreal Canadiens, Edmonton Oilers, Philadelphia Flyers, Carolina Hurricanes and the Boston Bruins.

Kovalenko was traded from the Colorado Avalanche to the Montreal Canadiens with Jocelyn Thibault and Martin Ručinský for Patrick Roy and Mike Keane.

In 1996, he scored the final goal in the history of the Montreal Forum, the fourth in a 4–1 victory over the Dallas Stars.

[2] In 1999, Kovalenko scored the first goal in the history of the RBC Center as a member of the Carolina Hurricanes in a 4–2 loss to the New Jersey Devils.

194, defeating long-time governor of Yaroslavl Oblast Anatoly Lisitsyn from left-leaning A Just Russia.