The Stars had tied the score on Tyler Seguin's goal with 52 seconds remaining in regulation play.
Jamie Benn scored on a backhand at 10:52 of the second to cut the deficit to 2-1.
The Devils, allowing the fewest shots per game of any NHL team, held Dallas to a season-low 16 shots. Cory Schneider made 15 saves for his second victory over the Stars this season.
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