The two teams were tied after 60 minutes and 80 minutes before Havlat scored 3:34 into the second overtime. San Jose leads the series 1-0.
The Sharks tied the game with just under six minutes remaining in the game on Andrew Desjardins' goal.
The Sharks victory against the No. 2-seed Blues brings back bad memories for Blues fans. St. Louis won the Presidents Trophy in 2000 but were upset by the No. 8 seeded Sharks in the first round.