The Kings had to fight back after squandering a two-goal lead in the third period, but Kempe scored his 13th goal on the rush from Viktor Arvidsson with 1:37 left in overtime to sweep their three-game homestand and get their fourth victory in a row.
Gabe Vilardi had a goal and an assist, and Phillip Danault and Blake Lizotte scored 10 seconds apart early in the third period for Los Angeles.
Tyler Toffoli had a power-play goal, and Dillon Dube and Jonathan Huberdeau also scored, but the Flames couldn’t get their third straight road win. Dan Vladar allowed four goals on 32 shots.
The Kings looked to be in control after a backhand goal from Danault 1:29 into the third period off a tenacious forecheck by Alex Iafallo, and Lizotte made it 3-1 by swatting in Vilardi’s rebound at 1:39.
Toffoli buried a wrist shot for his fifth power-play goal at 6:46 to pull within 3-2, and the Flames caught a break when Kevin Fiala put his penalty shot wide just over a minute later.
Calgary tied it at 3 with 6:28 to go when Dube netted his eighth goal off Noah Hanifin’s pass.
It was tied 1-all after the first period, with Vilardi striking late to cancel out Huberdeau’s sixth goal.
Vilardi tipped in his own rebound from close range with 2:19 to go after redirecting Sean Walker’s shot from the right point. Vilardi had not scored since Nov. 29, going 10 games without a goal but remained the team leader thanks to his hot start.
Huberdeau opened the scoring 3:23 into the game, beating Copley on a breakaway set up by Milan Lucic’s stretch pass. It was Huberdeau’s first goal and fifth point during a three-game streak.
The Kings activated F Brendan Lemieux from injured reserve on Thursday. Lemieux has not played since Nov. 12 because of a lower-body injury.
Flames: At Anaheim on Friday night.
Kings: At Arizona on Friday night.