Jeff Carter was getting booed by the opposing fans even before he scored from behind the goal line.
Carter, signed by Columbus as a free agent but traded last February, 39 games into his first season with the Blue Jackets, broke a 1-1 tie by scoring from behind the net. After goalie Steve Mason failed to control a rebound, Carter gathered the puck and flipped a shot that deflected in off the skate of defenseman Fedor Tyutin.
Carter was booed consistently by the crowd of 11,019 at Nationwide Arena.
"You just go out and you play your game," Carter said. "It's a huge game for us, for both teams. We both need wins, so it was a big one."
The defending Stanley Cup champions were coming off a 7-4 loss to the Anaheim Ducks and are now 3-3-2.
Voynov's goal made it 3-2 at 10:26. His long shot from inside the blue line on the right-wing boards sailed past two Blue Jackets on its way inside Mason's right post.
Carter's high-sticking penalty against Vinny Prospal gave the Blue Jackets a four-minute power play early in the third period, but Columbus managed just one shot on goal during the long advantage.
"I've talked about how your power play can create positive energy," Columbus coach Todd Richards said. "That four minutes were really just draining the clock. We spent more time working back to our zone than we did in the offensive zone. Our execution wasn't good. Credit to them and what they did, but we had to be better in that area. It was an opportunity we let slip away."
Kopitar tied the game in the opening minute of the second period before Carter's fluky goal. Columbus answered at 5:36 with a backhand goal from the slot by Derrick Broussard, who converted a pass from Tim Erixon.
Later in the period, Blue Jackets forward Brandon Dubinsky picked up 20 penalty minutes and Kings forward Mike Richards got 19 after fighting following Dubinsky's check of Scuderi into the end boards. Dubinsky received majors for boarding and fighting, plus a game misconduct.
Scuderi was shaken up but remained in the game.
Richards scored the final goal at 13:44 of the third, tipping in another goal-bound puck off Tyutin's skate from the crease. Justin Williams had his third assist.
"It's good to see [Williams] score points," Kings coach Darryl Sutter said. "It's good to see [Richards] score. Hopefully that's a step for them."
Information from wire services and team media was used in this report