Thomas Vanek had one shot on goal in 13:32 in his Blue Jackets debut after being acquired in a trade from the Vancouver Canucks on Monday.
Pearson ended a 15-game goal drought by tipping Drew Doughty's shot on the power play for a 3-2 lead at 16:33 of the second period. The Kings have scored at least one power-play goal in three straight games, going 4-for-12 with the man-advantage in that span.
"They score a big power-play goal to get their lead and we didn't," Blue Jackets captain Nick Foligno said. "It's going to be a special teams battle down the stretch, we knew that. And we got to find a way to make sure our penalty kill is as good as our power play, and vice versa."
Carter scored shorthanded, his third goal in four games after missing 55 with a lacerated ankle tendon that required surgery, to make it 4-2 at 8:22 of the third period.
Iafallo got his first multigoal NHL game when he scored to put the Kings ahead 5-2 at 16:43.
The Kings fell behind by two in the first period but tied the game with goals 2:23 apart early in the second. Thompson made it 2-1 at 2:48 on a long shot from the right face-off circle. Thompson's first goal since being acquired in a trade from the Ottawa Senators on Feb. 9 came 22 seconds after the Kings killed a hooking penalty on Iafallo.
"Having a good penalty kill and gaining momentum on the power play helped us a lot, so we got to keep doing that," said Iafallo, who tied it 2-2 at 5:11 when he tipped Folin's pass.
The Blue Jackets took a 1-0 lead 3:41 into the game when Atkinson scored. Panarin made a no-look backhand pass to Atkinson for a one-timer.
Jones put Columbus up 2-0 at 13:33.
"We lost our composure and didn't fully get it back consistently enough," Blue Jackets coach John Tortorella said.