Kurtis MacDermid scored, and Cal Petersen made 32 saves in his first win of the season for the Kings (3-2-2), who have won two in a row and three of four.
"I think I've kind of been better each performance, and now things are starting to come together a little bit," said Petersen (1-2-0), who made 13 saves in the third period. "Being able to win is the main thing, and so anytime I can do that I feel confident in my game."
Joel Eriksson Ek scored, and Kaapo Kahkonen made 19 saves for the Wild (4-3-0), who have lost two straight.
"I think [Los Angeles] made a pretty good job of taking away our speed in the neutral zone in the first period," said Eriksson Ek, who has scored three goals in the past four games. "We couldn't really get through. I think it got better in the second and third, but yeah, we want to get out there, we want to get that first goal and we couldn't do it today."