Dustin Brown also scored and Jonathan Quick made 32 saves for the Kings. Los Angeles is 3-1-1 in its past five games.
''They had a lot of opportunities that Quicke stood big and strong in the net,'' Kings coach Todd McLellan said. ''Wasn't a well-played game on our behalf, not a lot of detail. ... Not the way we want to play, but we found a way to win an ugly game.''
Mackenzie Blackwood had his six-game winning streak broken despite making 36 saves, and the Devils earned a point for the fifth straight game.
The Kings controlled the puck in overtime before Kempe buried a wrist shot from the wrist circle at 1:58 for his 11th goal of the season and 100th career point.
''The far side was kind of open and I haven't scored in a while, so it was time to shoot, you know?'' said Kempe, who went 18 games between goals since he scored twice against Vegas on Jan. 9.
Brown's goal at 13:14 of the second period tied it up at 1. Anze Kopitar pressured Devils defenseman Damon Severson into a blind backhand that was picked off by Alex Iafallo, leading to Brown's wrist shot in the slot to the short glove side.
The Devils took a 1-0 lead at 7:19 of the first period on Jesper Bratt's 15th goal. Bratt was in the right circle to bury a one-timer off Nikita Gusev's pass.
''I think his work ethic is getting better and better,'' Devils center Pavel Zacha said of Bratt, who has four goals in his past five games. ''He always had skill and the instinct to be on the ice and score goals, so I'm happy it's going for him the way that he wants it to. He deserved a few more goals at the start of the season, but he kept working and is getting rewarded now.''
Gusev's assist extended his point streak to five games. He has two goals and six assists in that span.
NOTES: Blackwood is 7-0-2 in his past nine starts. ... Kings D Mikey Anderson played 18:59 in his NHL debut. A fourth-round draft pick in 2017 and two-time NCAA national champion at Minnesota-Duluth, he is the younger brother of Devils F Joey Anderson. . The Devils recalled F Jesper Boqvist from the AHL on Saturday. He will join the team in Anaheim on Sunday. . Kings C Jeff Carter (lower body) missed his fifth straight game.
Devils: Visit the Anaheim Ducks on Sunday night.
Kings: Visit the Vegas Golden Knights on Sunday night.
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