Martin Hanzal netted the winner in the second period and Mike Smith stopped 21 shots to lead Phoenix over Minnesota, 2-1, on Monday.
Lauri Korpikoski registered the other goal for the Coyotes, who have won two in a row and are unbeaten in regulation in their last five outings (3-0-2).
Zach Parise scored and Niklas Backstrom made 32 saves in defeat for the Wild, losers in five of their last seven.
Hanzal struck at the 7:48 mark of the middle period to give the hosts a 2-0 edge.
Radim Vrbata let go of the initial shot from deep along the left wing, and, when Backstrom was unable to corral the rebound, Hanzal collected the disc and scored inside the right post.
Parise brought Minnesota within a goal at 10:20, converting a Phoenix turnover with a wrister from the left circle.
But that's all the visitors had in the tank. The Coyotes defense tightened up in a scoreless third period, and Smith needed to make only four saves to maintain that one-goal advantage.
Korpikoski opened the scoring with 4:51 to play in the first period, when he slid through the slot and skillfully redirected a point shot from Boyd Gordon.
The hosts kept the pressure on throughout the opening 20 minutes, but Backstrom made 16 saves to keep it a 1-0 game.