Mike Condon got the start in place of injured Carey Price, who is expected to miss at least six weeks with a lower-body injury. He stopped 22 shots for his ninth win.
Paul Byron scored his third goal for the Canadiens 2:51 into the game. Nick Foligno tied it at 17:23 of the first.
It stayed that way until Pacioretty, with Scott Hartnell in the box for tripping, scored his team-leading 13th goal of the season at 17:51 of the third period.
Montreal has won six of its last seven against Columbus.
Sergei Bobrovsky made 24 saves for Columbus.
Byron gave Montreal the early lead when he raced to the front of the net and tipped in a cross-ice pass by Christian Thomas past Bobrovsky.
Foligno tied it with a back-handed wrap-around goal after Condon got caught too far out of his net.
Defenseman Alexei Emelin's night ended early after a late hit on Matt Calvert earned him a five-minute major and a game misconduct at 17:57 of the first.
The puck was nowhere near Calvert when Emelin raised his shoulder and knocked the Columbus winger down in open ice. Calvert spent several minutes on his knees before going to the dressing room. He was back on the ice for the second period.
Emelin missed seven of Montreal's last eight games — five due to injury and the last two as a healthy scratch.
Columbus failed to score on the five-minute power play.
Things got even scrappier in the second when Foligno and Nathan Beaulieu dropped the gloves after the Blue Jackets captain knocked Tomas Fleischmann into the boards with a knee-on-knee hit.
Notes: Montreal's Michel Therrien coached his 700th NHL game. ... Brandon Dubinsky was back in the Columbus lineup after serving a one-game suspension for his hit on the Penguins' Sydney Crosby.