Kunitz switched from an apparent forehand shot to a backhander that got into the net over goalie Marty Turco, who had fallen to the ice.
The Stars' Jere Lehtinen had a chance to extend the shootout but his shot was blocked by Jean-Sebastian Giguere.
Mathieu Schneider had two goals for the Ducks and Giguere finished with 23 saves.
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