Couture scored in the first round of the shootout on a backhander that got past Dwayne Roloson. P.A. Parenteau's shot was high and after Joe Pavelski failed to score, Antero Niittymaki turned back a Frans Nielsen backhander and Dan Boyle beat Roloson on a backhander for the Sharks -- who won for just the second time in their last five games.
Boyle scored in regulation and Niittymaki finished with 24 saves for San Jose.
Parenteau scored a goal and Roloson finished with 37 shots for the Islanders, who have lost nine straight.