Artemi Panarin had a goal and two assists, Alex Laferriere had two assists and Darcy Kuemper made 30 saves for the Kings (1-4-2), who opened a five-game road trip.
Ryan Leonard and Cole Hutson each scored and Logan Thompson made 21 saves for the Capitals (5-4-0), who had won two straight.
Leonard gave the Capitals a 1-0 lead at 9:25 of the first period. He entered the zone, skated across the high slot and scored on a snap shot through a screen. The forward has points in six of his last seven games.
Hutson increased the lead to 2-0 with a power-play goal at 18:35. He eluded Laferriere at the blue line, skated down the slot and snapped a shot from the edge of the right circle.
The Kings, who had scored one goal in each of their past four games, tied it with two goals in 31 seconds during the final minute of the period.
Kempe scored first to pull the Kings within 2-1 at 19:27, taking a pass from Panarin on a 2-on-1 rush and scoring with a snap shot from the left face-off dot.
Panarin then tied it 2-2 at 19:58. Mikey Anderson forced a turnover by Capitals forward Jonny Brodzinski along the left wall and Panarin fired the loose puck past Thompson from the left circle.
Erik Gustafson gave the Kings a 3-2 lead at 7:28 of the third period with a power-play goal. He went end to end, split two Washington defenders at the blue line and deked Thompson before snapping a shot off the goaltender’s glove.
Kempe increased the lead to 4-2 when he scored at the right post when he converted a pass from Panarin behind the net at 11:35, and Scott Laughton scored into an empty net at 18:15 for the 5-2 final.
Kings forward Quinton Byfield left the game midway through the first period and did not return due to an upper-body injury.
