Devils goalie Johan Hedberg got a stick on Stuart's shot from the left circle but it bounced off him and into the goal with 6:47 left in the game, breaking a 2-2 tie.
Ondrej Pavelec made 23 saves as Winnipeg won for the fifth time in six home games.
Adam Henrique and Patrik Elias found the net and Hedberg stopped 16 shots for the Devils.
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