Arizona (38-33-8), which scored more than two goals for the first time in eight games (2-3-3), is one point behind the Colorado Avalanche for the second wild card into the Stanley Cup Playoffs. Josh Archibald had two goals and an assist, and Darcy Kuemper made 39 saves for his fifth shutout of the season.
"He looks big in the net, and calm," Coyotes coach Rick Tocchet said of Kuemper, who made his 20th consecutive start. "A lot of guys are feeding off him. He's calm on the off days, he's calm during practice, and he's calm during games. That exudes a lot of confidence to your players."
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The Coyotes, who haven't made the playoffs since 2012, are 10-1-1 in their past 12 home games.
"We need some help," Kuemper said. "We need Colorado to lose, but we feel if we win these final three games, we have a good chance."
Minnesota (36-34-9), which has lost eight of its past 11 games (3-7-1), remained four points behind Colorado. Devan Dubnyk made 19 saves.
"You've got play to the end of the season, but yeah, this was a big game," Wild forward Marcus Foligno said. "It was a chance to put these guys in our rearview mirror and look at Colorado, but now we still have that gap between us and Colorado. This was a big one and it hurts quite a bit."
Alex Galchenyuk gave the Coyotes a 1-0 lead at 7:48 of the first period. Nick Cousins won a face-off back to Oliver Ekman-Larsson, whose shot from the left point was saved by Dubnyk before Galchenyuk jammed the rebound in through his pads.