Kempe came off the bench, took Artemi Panarin’s pass and scored on a slap shot from the left circle after Kirill Marchenko’s power-play goal tied it 4-4 for Columbus with 1:56 remaining in the third period, a wrist shot from the left circle.
Brian Dumoulin had a goal and two assists, and Panarin and Scott Laughton each had a goal and an assist for the Kings (26-23-14), who had lost seven of nine (2-6-1). Anze Kopitar had an assist to extend his point streak to four games, and Anton Forsberg made 28 saves.
Los Angeles began a five-game road trip by moving within one point of the Seattle Kraken for the second wild card into the Stanley Cup Playoffs from the Western Conference.
Conor Garland scored twice, and Denton Mateychuk had a goal and an assist for the Blue Jackets (32-21-10), who extended their point streak to six games (3-0-3) and are 13-2-3 since Rick Bowness took over as head coach on Jan. 12. Jet Greaves made 26 saves.
Columbus pulled within two points of the Boston Bruins for the second wild card in the Eastern Conference.
The game, originally scheduled for Jan. 26, had been postponed because of heavy snowfall during Winter Storm Fern.
Laughton gave Los Angeles a 1-0 lead at 6:46 of the first period after scoring from the crease on Dumoulin’s centering pass. It was his second goal in as many games since being acquired in a trade with the Toronto Maple Leafs on Friday,
Panarin extended it to 2-0 at 14:48 from the top of the left circle on a wrist shot.
Garland cut it to 2-1 at 1:35 on a sharp-angle shot from below the right circle. Garland was acquired from the Vancouver Canucks on Friday, and it was his first goal and point in two games for the Blue Jackets.
Garland had not scored since Dec. 16 in the Canucks’ 3-0 win at the Rangers, ending a 24-game goal drought.
Mateychuk tied it 2-2 at 10:53 of the second period on a backhand from the right half wall through traffic.
Garland put Columbus ahead 3-2 at 12:13, keeping the puck on a 2-on-1 break before beating Forsberg with a wrist shot from the right circle.
Kempe tied it 3-3 at 14:09 by putting in the rebound of Dumoulin’s shot from the blue line, which took a redirect off Kopitar’s skate.
Dumoulin put Los Angeles back in front 4-3 at 10:07 of the third on a wrist shot from the slot following sustained possession in the offensive zone.