Mats Zuccarello and Frederick Gaudreau scored for Minnesota (24-14-4), which has won two in a row.
"We were happy with our patience in the hockey game," Wild coach Dean Evason said. "They played hard. They kept coming. It's almost like they play pretty freely, and offensively their [defensemen] jump into the play.
"But we were happy that we didn't deviate. We stayed with what we thought was going to give us a chance to have success tonight, and ultimately it did."
Lawson Crouse scored, and Connor Ingram made 25 saves for Arizona (13-24-5), which is 0-8-0 during the losing streak.
"We played a really good game against a really good team," Coyotes coach Andre Tourigny said. "They're top five in the League for shots against them in the slot, and we had a lot tonight. We got rebounds, we got penetration, we defended well. … We defended with a lot of pride."
Zuccarello made it 1-0 at 9:39 of the second period during a 5-on-3 power play. He scored on a redirection after Kirill Kaprizov fed him coming through the slot.
"It's always nice to get some power-play goals," Zuccarello said. "We try to score every time we're out there. Sometimes it doesn't work. Sometimes it works. It's always nice to get a PP goal."