Jordan Greenway scored and Jared Spurgeon had two assists for Minnesota (22-18-3), which hadn't won at home since Dec. 13 (0-3-1 in previous four). Devan Dubnyk made 26 saves.
"We played a great game start to finish," said Dubnyk, who has won four consecutive starts. "We were pushing hard through the first two periods, and if we went down a man, the penalty kill was incredible. I don't know if I even got but a few shots on the power play, but just a ton of blocks and really smart play positionally.
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"And then, when you get a two-goal lead in the third period, you're allowed to defend, and we did a great job defending and doing it hard."
Brandon Tanev and Mark Scheifele scored for Winnipeg (27-14-2), which had won two straight. Connor Hellebuyck made 19 saves.
"We looked a half step slow at times with our offense," Jets coach Paul Maurice said. "Even down 2-0, you just felt that you just needed to stay in the game and we needed something to go in the third."
Greenway gave the Wild a 1-0 lead after receiving a pass from Eric Staal from behind the net and beating Hellebuyck under his arm at 5:40 of the first period.
Zucker redirected a pass from Mikko Koivu on the power play to extend the lead to 2-0 at 11:04 of the second period. He made it 3-0 at 17:50 on a breakaway after exiting the penalty box and receiving a lofted stretch pass from Zach Parise.