Carolina forward Max Pacioretty left in the first period after sustaining a lower-body injury. It is unrelated to his previous Achilles injury that caused him to miss the first 38 games of the season. There was no update after the game.
Sean Kuraly and Johnny Gaudreau scored, and Joonas Korpisalo made 35 saves for the Blue Jackets (12-27-2), who have been outscored 13-5 in three straight losses, including 6-3 to the Tampa Bay Lightning on Tuesday.
"We're finding ways to have good pockets, but we can't fall asleep and have lapses," Kuraly said. "It's something we're trying to work on, but it is frustrating."
Pesce gave the Hurricanes a 1-0 lead at 2:34 of the first period with a shot from the half wall for his first goal since Nov. 29.
Burns made it 2-0 at 10:39, scoring on a wraparound during a 4-on-4.
"We take a lot of pride in our defensive abilities, but to join in and contribute on the offensive side is awesome," Slavin said.
Kuraly cut it to 2-1 at 15:00 with a shot from the slot after receiving a pass from Mathieu Olivier who carried the puck around the net.
Jalen Chatfield restored Carolina's two-goal lead at 15:52 of the second period with his first NHL short-handed goal. The defenseman sped down the right side, cut towards the net and lifted the puck on his backhand to make it 3-1.
"The power play is supposed to create momentum," Gaudreau said. "Whether you score or don't score, you want momentum."
Pesce extended the lead to 4-1 at 8:02 of the third period, scoring on a rebound in front for his first multigoal NHL game.