James van Riemsdyk led a Toronto offence that ended a three-game losing streak with a goal and two assists.
The Stars' four-game winning streak ended when they were shut out for the first time since Jan. 9 at New Jersey.
Nazem Kadri opened the scoring with a goal 55 seconds into the game, and assisted when van Riemsdyk scored at 6:21 of the second period.
Phil Kessel had two assists, the second on Tyler Bozak's power-play goal at 10:30 of the second. Mike Santorelli finished the scoring with an empty-net goal at 16:09 of the third.
Bernier's save total was one short of his season high. He has nine career shutouts.
Dallas' Kari Lehtonen allowed three goals and stopped 22 shots.
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