The Sharks were holding onto a 2-1 lead as the second period was winding down but Couture produced a power-play goal with 5:01 remaining and Thornton soon followed to put San Jose in control.
Michael Handzus and Joe Pavelski delivered first-period goals for the Sharks and Ryane Clowe added a third-period tally. After averaging less than two goals per contest over an eight-game stretch, the Sharks have scored 11 times in their last two outings.
Thomas Greiss made 19 saves to get the win. Richard Bachman was roughed up for five goals on 37 shots.
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