Joe Pavelski deflected a blazing one-timer off the stick of Brad Stuart into the net at 14:23 of the third period to tie the score 2-2, and Logan Couture followed 30 seconds later with a wrist shot that decided the game.
Raffi Torres also scored for the Sharks, who raised their point total to 57 and moved into a tie for fourth place in the Western Conference with the Stanley Cup champion Los Angeles Kings.
Antti Niemi notched 24 saves for the Sharks, who won their fourth game in their last five starts.
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