Alex Newhook and Cole Caufield scored, Matheson had two assists and Sam Montembeault made 26 saves for the Canadiens (10-10-2), who went 3-2-0 on a five-game road trip.
Patrik Laine and Yegor Chinakhov scored, and Elvis Merzlikins made 27 saves for the Blue Jackets (7-13-4), who had won three of four after a nine-game skid (0-7-2).
Columbus played three games in four days and four in six.
“I saw a lot of mental mistakes tonight,” Blue Jackets coach Pascal Vincent said. “Just not as sharp, right? Just not connected. We had a decent start. Not great. The second period, we had some push there. But overall, you could feel it the whole game. It wasn't as connected, the intensity.”
Laine gave Columbus a 1-0 lead at 3:40 of the second. He picked up the puck in the neutral zone and skated past three defenders before scoring on the forehand during 4-on-4 play.
Newhook tied it 1-1 at 7:36 from the slot after a shot by Kaiden Guhle caromed to him.
“There’s times in the first we dominated, and they pushed back,” Caufield said. “It’s a game of runs, to be honest with you.”
Chinakhov regained the lead for the Blue Jackets at 9:47 with his second goal in as many games. After the Canadiens couldn’t clear the zone, Zach Werenski passed to Dmitri Voronkov at the left post. He sent a pass through the crease, and Chinakhov scored before Montembeault could slide across to cover to make it 2-1.
But Columbus couldn’t sustain the momentum.
“We had to be in our [own] zone for extended periods of time, just got to be able to answer those pushes that the other team has and not crumble like we’ve kind of done this year,” Laine said.
Caufield tied it 2-2 at 14:08. Merzlikins couldn’t corral the initial shot by Christian Dvorak and Caufield scored on the rebound.
“Playing fast in the neutral zone and kind of keeping them in, it’s huge for us momentum-wise,” Caufield said. “I think we did that a few times, and it paid off.”
Gustav Lindstrom scored an empty-net goal with 57 seconds left for the 4-2 final.
The Blue Jackets were unable to build on their 5-2 win against the Boston Bruins on Monday.
“It's a 2-2 hockey game going into the third period, and I just didn't think we pushed hard enough,” Werenski said. “We're in no position to let points like that slip. I just think we had a lot more to give in here and we didn't give it, and it's frustrating, especially coming off a big win against Boston, having a day off yesterday.”
NOTES: Caufield, in his 145th NHL game, became the fifth Canadiens player who has debuted in the past 100 years to score 60 goals prior to his 150th game. He joins Howie Morenz (74 games), Maurice Richard (83), Jean Beliveau (132) and Joe Benoit (135). … With an assist on Chinakhov's goal, Werenski set a Blue Jackets record for most assists in a month by a defenseman (11); he broke a tie with Seth Jones (February 2021), James Wisniewski (January 2014), Ryan Murray (January 2014) and Ron Hainsey (December 2006).
