Christian Fischer and Alex Goligoski scored, and Darcy Kuemper made 19 saves for the Coyotes (20-21-5), who lost for the sixth time in seven games.
"We've got some guys who are struggling for us, they're really struggling, they're not scoring, and they're not defending right, and it's hurting us," Arizona coach Rick Tocchet said.
The Wild are in third place in the eight-team Honda West Division, five points behind the second-place Colorado Avalanche. The Coyotes are in fourth, 14 points behind the Wild and one point ahead of the St. Louis Blues, who have three games in hand. The top four teams qualify for the Stanley Cup Playoffs.
"We've talked about not wanting to be a team that's waiting down to the last game to get in there. … We want to be sitting comfortable going into the playoffs," Minnesota forward Marcus Foligno said. "The goal is just to pick up momentum and keep getting the wins."
The Wild went 2-for-3 on the power play against the Coyotes, whose penalty kill has allowed six goals in seven opportunities in the past three games.
"It's definitely cost us some games here, cost us some points," Goligoski said. "It seems like they get that one look and it's in the back of our net. We're giving these power plays a little bit too much respect and time and space."
Jordan Greenway scored on Foligno's pass from the right face-off circle to put the Wild ahead 2-1 at 3:37 of the second period. It was his first goal in 22 games.
Marcus Johansson scored on a power play with a backhand in front off a Dumba rebound to make it 3-1 at 9:38.
Minnesota, which was 3-for-50 on the power play (6.0 percent) in its first 13 games, has scored 15 power-play goals in the past 10 games.
"Something that's great about our team right now is the power play," Foligno said. "It's been awesome, and you're seeing it on the scoreboard. … Right now, we're clicking, and I don't think we're even at a peak yet."