The victory moved San Jose into seventh place in the Western Conference, one point ahead of the Phoenix Coyotes. Couture's goal broke a 2-2 tie and proved to be the eventual game winner.
Antti Niemi shut out the Stars in the third period while the Sharks added two more insurance goals. Niemi finished with 29 saves.
Brenden Morrow and Alex Goligoski scored for the Stars, who trail Phoenix by two points in the battle for the final playoff slot in the Western Conference. Kari Lehtonen gave up four goals on 25 shots.