Brett Pesce, Vincent Trocheck, Jordan Staal and Dougie Hamilton each recorded a goal and an assist. Brock McGinn and Warren Foegele also scored for the Hurricanes, who won for the sixth time in seven games.
The game was tied four times until Staal's power-play goal put Carolina up 5-4 at 5:33 of the third period, and Hamilton's floater over Joonas Korpisalo midway through gave the Hurricanes a two-goal lead.
Patrik Laine's second goal, with 57 seconds left in the game, got the Blue Jackets within one again, but they couldn't tie it again despite a late power play.
''I liked how we just kept coming back,'' Carolina coach Rod Brind'Amour said. ''It felt like we get one, they get one. We'd get behind, and I feel like we didn't stop playing. It was always, `don't worry about it, let's get the next, one next shift' mentality.''
Riley Nash, Nick Foligno and Max Domi also had goals for Columbus, and Korpisalo had 20 saves.
Laine opened the scoring with a shot from the top of the left circle on a power play 10:07 into the game.
The Hurricanes tied it 25 seconds later when Andrei Svechnikov, who had been in the box for tripping on the Columbus goal, took the puck away from defender Vladislav Gavrikov at the goal line and fed a charging McGinn.
Nash got credit for the goal that made it 2-1 later in the first when a hard one-timer from Foligno grazed Nash on the way to the net.
Foegele's tap-in of his own rebound tied the score again in the second period. The Jackets' first shot in the frame came at 14:24 when Foligno got a breakaway and connected for the 200th goal of his NHL career.
Carolina tied it again late in the second with Pesce's long shot through traffic. They got their first lead of the game when Trocheck put back a rebound.
Domi's one-timer from the right circle early in the third period knotted the score again. Staal and Hamilton then gave the Canes their first two-goal lead midway through the period before the Columbus rally came up short.
''You never try to get in a battle with another team,'' said Hurricanes forward Ryan Dzingel, who had two assists.
''We're trying to keep things low scoring. I think when you have two teams that are very similar, the way they want to play and the way we want to play clashes sometimes. I think we're both very similar teams trying to get get pucks deep and get our D involved, hard-nosed and simple, so I think it was just one of those weird ones that turned out that way,'' he said.
After Trocheck scored late in the second period, officials overrruled an offside challenge by Blue Jackets coach John Tortorella after looking at the replay. The Blue Jackets were assessed a penalty because of the failed challenge. At the break, officials decided that the play was offside, after all. They waved off the last 45 seconds of the power play but didn't take the Carolina penalty off the board.
A usually outspoken Tortorella didn't have much to say. ''You know what? I'm going to let the league explain it,'' he said.
''I just think it's a bad look for the NHL to not get it right,'' Foligno said.
''I don't really understand it,'' Brind'Amour said. ''I'm glad it worked for us.''
Hurricanes: Eleven players notched points against Columbus. ... Svechnikov has point or more in seven of the nine games. ... Pesce has five points in the last four games. ... F Martin Necas was out after falling hard on his head late in Thursday's loss to Chicago.
Blue Jackets: The Blue Jackets put defenseman Zach Werenski on injured reserve Saturday with an unspecified lower-body injury. ... Laine has three goals in the last two games. ... F Jack Roslovic has points in the last four games. ... F Mikhail Grigorenko, who had a two-game point streak, was a healthy scratch for the first time this season.
The same teams wrap up a back-to-back series on Monday.
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