Werenski made it 2-0 at 5:24 when scored on a rebound of a Kirill Marchenko shot. It was his 300th NHL point.
Kotkaniemi cut in from the right circle to make it 2-1 at 7:10 before Teravainen tied it 2-2 at 18:16 following a drop pass by Kotkaniemi.
James Malatesta, who scored his first NHL goal in the previous game against the Nashville Predators on Saturday, gave Columbus a 3-2 lead at 19:01 off a pass by Olivier to the right post.
Teravainen tied it 3-3 at 10:16 of the second with a power-play goal.
Carolina forward Jesper Fast left with an undisclosed injury after going into the end boards after a cross-check by Erik Gudbranson at 1:16 of the second period. Brind’Amour did not have an update.
“That's the part that just makes you sick, to be honest with you,” Brind’Amour said. “You're just trying to get through the game without having that. I'm not sure where that's going to go.”
Forward Gavin Brindley, who helped Michigan reach the 2024 NCAA Frozen Four held last week, made his NHL debut for the Blue Jackets. He played 12:20 and had a shot blocked.
Forwards Bradly Nadeau and Jackson Blake, who played this season for the University of Maine and the University of North Dakota, respectively, each made his NHL debut for the Hurricanes. Nadeau was minus-3 with three shots on goal in 19:08, and Blake was minus-2 with two shots on goal in 15:18.
“It was a fun night,” Nadeau said. “Personally, we didn’t come up with the win but a lot of positives to take away from the game.”
NOTES: With an assist on the first goal, Werenski set the Blue Jackets record for the most by a defenseman in a season with 45, passing James Wisniewski (2013-14). With 57 points (11 goals, 46 assists), he tied Seth Jones (2017-18) for the most by a Columbus defenseman in a season. Werenski has 302 points (90 goals, 212 assists) in 486 NHL games.