Marchment has three goals in his first two games with the Blue Jackets after being traded to Columbus from the Seattle Kraken on Friday.
Kirill Marchenko scored on the power play, and Jet Greaves made 23 saves for the Blue Jackets (15-15-6), who won for the second time in their past nine games (2-6-1).
Columbus defenseman Zach Werenski did not play because of a lower-body injury he sustained blocking a shot against the Anaheim Ducks on Saturday.
Andrei Kuzmenko scored, and Anton Forsberg made 27 saves for the Kings (15-11-9), who have lost five of six (1-3-2).
The Blue Jackets went up 1-0 at 4:07 of the first period. Marchment skated through Joel Armia and Trevor Moore to get to the slot and put a wrist shot in off Forsberg’s blocker on the power play.
Columbus took a 2-0 lead at 19:36 on the power play when Marchment scored his third goal in two games. Boone Jenner’s shot from the high slot took a double deflection off Damon Severson’s stick and in off Marchment’s shoulder.
Los Angeles got within 2-1 at 18:41 of the second period on Kuzmenko’s wrist shot from the blue line through traffic.
Marchenko made it 3-1 at 14:16 of the third period again on the power play. The Blue Jackets were 3-for-7 on the man-advantage; the Kings were 0-for-5.