Pekka Rinne turned aside 28 shots for the red-hot Predators, who tightened their grip on the sixth seed in the Western Conference while improving to 92 points.
Dallas suffered a key loss in its bid to make the West's playoff picture. The Stars entered the game one point behind Anaheim for the eighth and final playoff berth with eight games remaining.
Alex Goligoski and Brenden Morrow scored and Kari Lehtonen stopped 28-of-31 shots for the Stars.
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