Couture's goal came after Mike Ribeiro was sent off for a high-sticking double minor penalty.
San Jose snapped a two-game skid and handed the Stars their fourth loss in six games. The one point Dallas earned, however, moved the Stars one in front of Anaheim for the lead in the Pacific Division.
Antero Niittymaki needed to make only 15 saves to get the victory. Kari Lehtonen, who had missed the four previous games with a back injury, stopped 39 shots.
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