Joel Eriksson Ek and Marcus Foligno each had a goal and an assist for the Wild (51-22-7), who were 8-0-2 in their previous 10 games. Marc-Andre Fleury made 21 saves.
Minnesota, which has two regular-season games remaining, and the St. Louis Blues each have 109 points; the Blues, who have seven more regulation wins, have one game left after a 5-3 loss to the Colorado Avalanche on Tuesday.
"Our whole game [stunk] tonight," Wild coach Dean Evason said. "We got what we deserved. That hasn't happened to us, fortunately, and we didn't shoot the puck. We were just going through the lineup and you don't go through everybody, but it's hard to find a good player here tonight."
Anton Stralman had a goal and two assists, and Jack McBain scored his first NHL goal for the Coyotes (23-50-7), who had lost 10 straight games (0-8-2). Karel Vejmelka made 35 saves.
"We lost our mojo for a 10-day period, and it was not pretty," Arizona coach Andre Tourigny said. "You never know if you will get it back. It's not a guarantee. It's not easy. If it was easy, everybody will have it. You see the guys fighting like that at the end when it's easy to just pack in, I'm really proud of them."