Marek Zidlicky scored twice for the Wild, his first two goals of the season.
Ilya Bryzgalov stopped 28 shots for Phoenix, which had a three-game winning streak come to an end.
Zidlicky scored on the power play at 3:28 of the second for the game's first goal. His other goal came with 67 seconds left in the third.
Minnesota has beaten Phoenix nine straight times and 11 out of 12. The Coyotes suffered their second shutout of the season.
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