Havlat's slap shot, producing his second goal of the game, ended a tense goaltending duel between San Jose's Antti Niemi and the Blues' Jaroslav Halak. Havlat scored the 20th and 21st playoff goals of his career and his first since 2009 when he was a Chicago Blackhawk.
San Jose needed a goal from Andrew Desjardins with 5:16 to play in the third period to tie it, after which Niemi took over in a 40-save performance.
Havlat gave the Sharks the lead early in the second period, but the Blues moved in front on two goals from Patrik Berglund during the first 7:30 of the third.
Niemi has won 24 playoff games over the last two seasons, leading San Jose to the conference finals both years.
Halak stopped 31 shots. St. Louis will host the second game of the series Saturday.