Steven Kampfer added an empty-netter for the Wild, who played without stars Zach Parise, Mikko Koivu and Ryan Suter.
Bryan Little had Winnipeg's only goal.
Dumba set the tone when he jumped on a loose puck and beat Al Montoya at 7:45 of the first. The Jets then tied it when captain Andrew Ladd intercepted a sloppy pass and found Little, who flipped a backhander past Josh Harding.
The Wild responded with two goals in the second to grab control.
Montoya made 29 saves while Harding finished with 16. Darcy Kuemper replaced Harding in the third and had 11 stops.