Adrian Kempe scored his 17th goal to set his NHL career high, and Philip Danault scored twice for the Kings (20-13-5), who have won four in a row and eight of 11. Cal Petersen made 17 saves to win his third in a row.
"It was a battle, a fight for ice both ways," Los Angeles coach Todd McLellan said. "They checked hard, they closed the gaps. They took space away and won some races to the pucks. We did the same thing. Very tight game, and then both goaltenders made some good saves when they had to."
Chris Driedger made 19 saves making his second straight start for the Kraken (10-23-4), who haven't won since Dec. 14 and have lost 12 of 13 since Dec. 3.
"It's just really frustrating in our situation right now," Driedger said. "Trying to get a win. My job is to get wins and let in less goals than the other guy. I haven't been able to do that in the last two matches. I definitely think my game could have been better. You can never be satisfied, especially at a time like this. … It's completely unacceptable to drop nine in a row."
The Kings took a 1-0 lead when Kempe scored at 4:06 of the first period. Alex Iafallo's shot rebounded off Driedger, and Kempe stopped the puck with his skate then knocked it in to extend his point streak to four games (three goals, one assist).
Kempe's previous NHL high was 16 goals in 81 games in 2017-18, his second season.
"I think Adrian has matured, not physically, but just the way he understands the game better," McLellan said of the 25-year-old. "He anticipates things better, he's in the right spot. His shot's improved. He works as hard away from the puck and checking as he does offensively, and as a result he's getting a lot of chances. He's got a lot of skill and talent. So we're really happy for him."