Korpikoski scored his fourth goal -- all against Finnish goaltenders -- in the first period, and Hanzal got his third in three games in the second. Smith was sharp for the second straight start, giving up a goal on a turnover in the second period and fighting off a power play by the Wild in the closing minutes.
Zach Parise scored his 200th career goal, and Niklas Backstrom stopped 32 shots for Minnesota. The Wild went more than 15 minutes without a shot spanning the second and third periods and hit the post twice to remain winless on the road this season (0-3-1).
After a shaky start to its defense of last year's Pacific Division crown, Phoenix has rounded back into defense-first form.
Clogging shooting lanes and diving in front of pucks, the Coyotes have made their end of the ice claustrophobic for opposing teams again, allowing five goals during a four-game point streak after allowing 20 in the first five games.
Phoenix helped Chad Johnson earn his first NHL shutout against Nashville, and Smith looked a lot more like the goalie who led the Coyotes to last year's conference finals in his last start. He turned away 17 shots against Dallas for his 20th career shutout on Saturday.
Coming off a lackluster loss to Anaheim, the Wild shook things up before Monday's game, trading forwards Darroll Powe and Nick Palmieri to the New York Rangers for tough-guy forward Mike Rupp.
Minnesota had to wait for Rupp, though; the veteran who scored the Stanley Cup-winning goal for New Jersey in 2003 wasn't able to join the team in time to play against the Coyotes.
The Wild also called up heralded rookie Charlie Coyle from the AHL and shook up their lines in hopes of getting a spark.
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The changes didn't do much good against the Coyotes early.
Phoenix created some good chances, and Smith was solid again, stopping Zenon Konopka's backhander from in close early, then poke-checked the puck away from Kyle Brodziak before he could get a shot off on a short-handed breakaway. He also got some help from defenseman Keith Yandle, who slid across the crease to make a toe save with Smith in a prone position.
Yandle made another impressive play right after that, gloving down the puck near Minnesota's blue line and firing a shot that Korpikoski redirected past Backstrom. Korpikoski, from Finland, has scored all four of his goals this season against Finnish goalies: Backstrom, Kari Lehtonen, Antti Niemi and Pekka Rinne.
Hanzal made it 2-0 midway through the second period, flipping in a backhander past a sprawled-out Backstrom after a hard shot by Radim Vrbata bounced off the Wild goalie.
Minnesota got its forecheck going after that, though, creating a turnover in Phoenix's zone. Parise ended up with the puck after it bounced off Coyotes forward Mikkel Boedker's skate and beat Smith with a wrister from the left circle for his sixth of the season.
But that was it for the Wild. Jonas Brodin hit the right post midway through the second period, and Pierre-Marc Bouchard did the same in the third during a late power play.
NOTES: Phoenix C Matthew Lombardi skated with the team Monday morning, but still isn't ready to return from a shoulder injury that has caused him to miss six games. ... Wild D Nate Prosser was a healthy scratch for the fifth straight game after playing the first four games of the season. ... Coyotes D David Schlemko left the ice for the dressing room in the first period, holding his right shoulder. He didn't return.
Press; By JOHN MARSHALL]
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