A slow start and inconsistent play allowed Phoenix to jump out to an early 1-0 lead in the first throwing 15 shots on goal in the first period compared to Minnesota's five.
A new look Phoenix team under new coach Dave Tippet carried most of the momentum throughout the first two periods with an aggressive forecheck and great puck control in the offensive zone, exactly what Minnesota is trying to do.
The Coyotes kept Wild goaltender Niklas Backstrom busy by shooting from anywhere on the ice and often finishing the game with 32 shots on goal.
The real let down came in the third period when Antti Miettinen scored at 15:02 to tie the game at two and just 19 seconds later Phoenix's Scottie Upshall scored from a tough angle to take the lead for good and seal the win for the Coyotes.
Phoenix did have a fast start to the season but since has dropped to a 12-9-0 record two points behind Dallas for third place in the pacific division with 24 points.
Minnesota falls to 7-12-2 overall, 5th in the northwest division and 14th in the western conference.
Minnesota drops the first of a four-game homestand which will continue on Friday as the Wild host the Islanders.