Alex Turcotte also scored, and Darcy Kuemper made 18 saves for the Kings (24-10-5), who have won five straight.
Kuemper stopped Kyle Connor’s wrist shot from the high slot 20 seconds before Kempe scored.
“The save [Kuemper] made on Connor obviously is the one that gives us a chance to come down and get the game,” Los Angeles coach Jim Hiller said. “We played well, and right from the start we were on our game. I was worried about it for a lot of different reasons; we talked about some of them. Proud of them. They came out and played hard in a really tough building against a really good team.”
Mark Scheifele scored for the Jets (28-12-3), who have lost four of five (1-2-2). Eric Comrie made 21 saves.
“It was a hard-fought game,” Scheifele said. “Both sides protected the inside ice and didn't give much easy ice inside. So it was a tough battle right till the end. … We still had some chances, we still had some opportunities to score some goals. But they're a tough team there. They play solid D, they make it tough to get the inside. They have good sticks, so they made it tough.”
Jordan Spence appeared to give Los Angeles a 1-0 lead 4:01 into the first period, but the goal was overturned after the Jets challenged for offside.
"That's as close to a playoff game as we've seen so far,” Winnipeg coach Scott Arniel said. “That's exactly the type of game that gets played at the end of the season. Not a lot of room to make plays. When you did have some time, it got closed off pretty quick. Both teams, for us, we tried to defend the guts of the ice and you saw it both ways.”
Turcotte made it 1-0 for the Kings at 4:39 of the second period. Kempe threw the puck toward the net from the point, and Turcotte tipped it from the left hash marks.
“I think we played them really well the first 40 minutes,” Kempe said. “We kept them on the outside, not that many high-danger chances, so that's something that we're really happy with. But obviously it's hard to keep doing it for 60 minutes, especially when you're up one goal.”