Rasmus Kupari, Drew Doughty and Trevor Moore also scored for the Kings, who netted three power-play goals in a span of 2:19 late in the third period after Edmonton's Connor McDavid was given a boarding major for hitting Kempe from behind.
''We just stuck to our game plan, we didn't sit back, kept pushing forward,'' Doughty said. ''Our game plan is never to take a lot of high risks, just to stay calm, get pucks in and get pucks out. ... we didn't want to change anything in the third, we didn't want to sit back.''
Darnell Nurse scored the lone goal for the Oilers, who lost two straight for the first time this season. Mikko Koskinen stopped 35 shots.
''This has been coming for a while here, been coming for a while,'' Oilers coach Dave Tippett said. ''We've been masking it with some special teams stuff, but we haven't had enough guys play well for a while. It was a 2-1 score but weren't good enough in it, and we gave up some power-play goals at the end.
''We've got too many guys who aren't contributing enough to help us here.''
The Oilers got off to another bad start, as the Kings scored just two minutes in when Moore made a nice touch pass to Kupari at the side of the net for an easy tap-in past Koskinen.
The Kings made it 2-0 less than two minutes into the second period, with Kempe scoring his ninth on a wrist shot that Koskinen could have saved.
Edmonton got back into the game midway through the second period with a shorthanded goal. Nurse scored his first of the season, up high from a sharp angle past Quick. It was Nurse's first game back after missing six due to breaking a finger when he blocked a shot.
A late comeback became more difficult for the Oilers with McDavid's five-minute major with 6 1/2 minutes remaining in the third period. Los Angeles got a power-play goal just over a minute later by Kempe - his second of the game on a rebound from the doorstep.
The Kings added a second goal on the man-advantage as Doughty was able to rifle a shot into a wide-open net, and less than a minute later, Moore found some space in front to beat Koskinen.
NOTES: Mike Smith (lower body), Devin Shore (lower body), Slater Koekkoek (lower body), and Duncan Keith (upper body) were all out for the Oilers, while Cody Ceci remained out under COVID-19 protocol. ... The Kings were missing two players due to COVID-19: Andreas Athanasiou and Blake Lizotte. . Kings forward Brendan Lemieux served the third of a five-game suspension for biting Ottawa Senators forward Brady Tkachuk.
Kings: At Vancouver on Monday.
Oilers: Host Minnesota on Tuesday for the second game of a six-game homestand.
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