The Tampa Bay Lightning picked up two big points in the standings, but may have lost three centers to injuries Thursday night.
Kucherov assisted a goal by Andrej Sustr, giving him nine goals and eight assists in his last eight games. Victor Hedman also scored, and Andrei Vasilevskiy made 32 saves. Vasilevskiy is 4-0-1 since the trade of Ben Bishop to Los Angeles, and the Lightning are 9-2-3 in their last 14 games.
"We're going to need more efforts like this one to get in (the playoffs)," Hedman said, "but obviously it's a step in the right direction."
Marco Scandella scored for Minnesota with 3:58 remaining, only the Wild's second goal in regulation in their last three games. Western Conference-leading Minnesota has lost three of four for the first time since early December. The loss also broke the Wild's streak of 10 straight wins after a loss.
Seven seconds after a tripping penalty on Ryan Suter, Kucherov scored his 29th goal of the season with assists from Ondrej Palat and Hedman. It was the first power-play goal against Minnesota in 12 games, ending a streak of 22 penalties killed.
Hedman made it 2-0 at 11:01 of the first period, scoring his 13th goal with assists from Jonathan Drouin and Jake Dotchin.
Sustr's goal, his second of the season, came at 4:37 of the second period. It was assisted by Kucherov and Tyler Johnson, who was helped off the ice four minutes later. Vladislav Namestnikov also left the game with an injury and Cedric Paquette was taken off with a left ankle injury midway through the third period. Those were sobering sights for a team trying to make a late run for a playoff spot.
"It puts a lot of pressure on other guys and it's never fun to see, to watch guys in pain and being carried off like that," defenseman Anton Stralman said.
"It doesn't sound encouraging for any of them, but . . . we'll see tomorrow," Lightning coach Jon Cooper said. "If we got one of them for Saturday, that would be a blessing."
Wild C Ryan White played in his 300th game. . . . D Matt Dumba (illness) missed his second straight game. ... D Christian Follin (upper body) is out. ... Lightning C Steven Stamkos (knee) continues to practice but no date is set for his return. ... RW Ryan Callahan (lower body) did not play.
Wild: Play at Florida on Friday night in the second game of a five-game trip.
Lightning: Play at home against Florida on Saturday night in their final meeting of the season against the Panthers.