Adrian Kempe scored for Los Angeles (36-21-9), which had allowed one goal in its previous three games. Darcy Kuemper made 19 saves.
The Kings remained one point behind the Edmonton Oilers, who have played one more game, for second place in the Pacific Division.
“We got a little sloppy in the third period,” Kings coach Jim Hiller said. “Second period I thought we played really well, a good period, and probably had enough chances to come out with the lead in the third. ... Gustavsson played very well, I thought. I don't know if anybody else saw that. We probably still turned up way too many chances where we had a chance to shoot with traffic. ... So, you know, one of those nights where, when we finally put it there, we didn't get anything. But yeah, it's a winnable game. It's a mistake. It's execution on their side at the end.”
Kempe gave the Kings a 1-0 lead at 4:59 of the first period, scoring a power-play goal with a one-timer from the right circle off a cross-ice pass from Kevin Fiala.
Wild defenseman Jon Merrill kept it a one-goal game at 12:00 when he lunged with his stick to deny Alex Laferriere's diving shot at an open net.
“A little bit of a breakdown, we were all kind of scrambling,” Merrill said. “We talked about coming into this game and doing whatever it took to get the win, playing desperate, being there for each other. That’s all I was trying to do is be there for [Gustavsson], and got lucky it hit my stick.”