Ryan Hartman, Mats Zuccarello and Jared Spurgeon scored for the Wild. Kahkonen won his ninth straight start during a standout rookie season.
Minnesota swept three consecutive home games against Arizona and extended its home winning streak to eight, the longest in the NHL this year.
''You know, everybody's doing their job, and you can rely on everybody doing their job,'' Kahkonen said. ''It's just really, really fun to see and really great to see, you guys, whether it's blocking shots or winning faceoffs or whatever it is, it's just going really well right now.''
Adin Hill made 23 saves for the Coyotes.
''There's guys stressed. Everybody's stressed when you don't score goals,'' Arizona coach Rick Tocchet said. ''We've had seven or eight breakaways in three games, we haven't scored. You get one there, maybe loosen some guys up, you can just tell, and then things snowball. . We're getting tested. People are testing us, adversity's testing us.''
Hartman scored his fourth goal 1:37 into the third straight game between the teams. The familiarity and a major penalty added to a chippy game. Carson Soucy was given a five-minute major for charging Conor Garland when he left his feet and made contact with Garland's head.
Lawson Crouse then initiated a fight as soon as Soucy left the penalty box. Crouse was given a penalty and game misconduct for instigating. The teams combined for 47 penalty minutes but were a combined 0 for 7 on the power play.
''We have to be desperate,'' Coyotes forward Christian Fischer said. ''We did a better job delivering pucks, up tempo, getting up ice, but that's only going to take you so far. You've got to have two or three guys in that crease pitchforking if it comes to it. We need to get greasy goals, we need to score, we need to do a lot. . We've got work to do. I leave it at that.''
Zuccarello got his fifth of the season in the third, the 4,000th regular-season goal in Wild history.
Zuccarello missed the first 11 games with an upper-body injury, but has 19 points in 16 games since returning and has been quite the match with NHL rookie scoring leader Kirill Kaprizov to pace Minnesota's offense.
The Wild are first in the league in wins, points and goals since Feb. 18, going 12-2-1.
''It's one of those feelings where we're excited to come to the rink every day,'' Hartman said. ''Every time we're getting ready to gear up for a game, we have the mindset that we're going to go out there and we're going to win the hockey game.''
Spurgeon added his first goal late in the third period.
KAHKONEN KEEPS ROLLING
Kaprizov isn't the only Minnesota rookie showing well.
Kahkonen's nine straight wins are the longest streak by an NHL netminder this year and he started the day sixth in the league in save percentage and eighth in goals-against average for goalies with at least 10 games.
''Likely as high as you can imagine,'' Wild coach Dean Evason said of his confidence in the team's goaltenders after Kahkonen returned to the net following two strong performances from Cam Talbot. ''Both guys, we feel extremely comfortable. Most importantly, is the team feels extremely comfortable. Yeah, it's nice obviously. Penalty kill, your goalie is your best penalty killer and clearly he was tonight.''
ARIZONA GOALTENDING WOES
Antti Raanta, who had taken over as the top goaltender for Arizona with Darcy Kuemper injured, was held out with a lower-body injury. The team said Raanta is day to day. Ivan Prosvetov was recalled from the taxi squad to serve as Hill's backup.
Niklas Hjalmarsson returned after missing one game with an upper-body injury. Arizona also recalled Hudson Fasching from the taxi squad to play in Tuesday's game. Michael Chaput was assigned to the taxi squad.
Coyotes: Continue their seven-game road trip Thursday at Anaheim where they play two games against the Ducks.
Wild: Travel to Colorado for a pair of games starting Thursday. The teams have split four meetings this season.
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