Kirill Kaprizov scored his 42nd goal, Matt Boldy and Jared Spurgeon each had a goal and an assist, and Marc-Andre Fleury made 31 saves for Minnesota (44-21-6), which had lost two straight and moved into a tie with the St. Louis Blues for second in the Central Division.
"We weren't playing bad," Fleury said. "The breakaway to start and the power play I should've saved. The second one I didn't see. It gave them momentum. I liked how everybody didn't panic. I think it shows the maturity of the group and the character of the group. We kept pushing to get the next goal, and we did and we went from there.
"The team that we have, I always have confidence that we can comeback in games, and we did tonight."
Cal Petersen made 27 saves for Los Angeles (38-26-10), which has lost three in a row and five of seven (2-4-1). The Kings lead the Vegas Golden Knights, who have one game in hand, by two points for third place in the Pacific Division.
"You score a power-play goal, you score a shorthanded goal, you get a 3-0 lead on the road, there's no reason why you're not in it at the end of the night, and we weren't," Kings coach Todd McLellan. "Really disappointing."
Los Angeles scored on three of its first five shots.
Rasmus Kupari made it 1-0 with a shorthanded goal at 1:33 of the first period. Trevor Moore sent a backhand pass into the zone for Kupari, who got behind Frederick Gaudreau and chipped a shot over Fleury's blocker.
"I wasn't happy with myself to start the game but loved how the guys responded and kept playing," Fleury said. "We got some big goals to make the game close right away in the first. Then to score six is always a big help."
Carl Grundstrom increased the lead 2-0 at 8:22, working the puck out from behind the net and scoring with a backhand from the left circle, and Adrian Kempe made it 3-0 at 10:17 with a one-timer from the top of the right circle on the power play.
"That third goal goes in, not going to lie to you, as a coach and a head coach, you go maybe the group needs a little twist here to wake us up," Wild coach Dean Evason said. "You can call a timeout and yell at them, and we don't like to do that. You want them to try to figure it out, or you can pull the goalie and it snaps them into place. … But we knew [Fleury] was going to compete his butt off after that. He almost broke his stick. … You knew he wasn't happy with it. He's accountable for it and he's been through it. Same as we allow our team to figure it out, we don't call a timeout to yell at them. We trust that they'll figure it out. We trust that Marc-Andre Fleury will figure it out, too."
