Harvey-Pinard responded 13 seconds into the second period to give the Canadiens a 3-2 lead, knocking in a loose puck in the crease. He then extended it to 4-2 at 7:13 off a rush.
Gallagher pushed it to 5-2 at 13:08 when he scored from the slot after receiving a centering pass from below the goal line by Jake Evans.
Harvey-Pinard completed the hat trick to make it 6-2 at 16:42, deflecting a slap pass from Hoffman for a power-play goal.
"Honestly, it's tough to describe," said Harvey-Pinard, who was playing in his 33rd NHL game. "I had chills."
Harvey-Pinard is the first NHL rookie to score three goals in a period since Kirill Kaprizov of the Minnesota Wild did it against the Arizona Coyotes on March 12, 2021.
"He's very engaged at both ends of the ice," Montreal coach Martin St. Louis said. "It's rare that he doesn't do his job defensively and offensively. He's a young player who is very engaged and who reads the play well at both ends of the ice. It's not just where the puck is, but where his teammates are as well and where the opponent is going."
Alex Belzile extended it to 7-2 at 11:48 of the third period, finishing a give-and-go with Chris Tierney, and Suzuki scored at 13:49 for the 8-2 final.
"We had no push back and they took it to us," Blue Jackets forward Boone Jenner said. "That's what's going to happen in this league."
NOTES: Harvey-Pinard is the fifth rookie in Canadiens history to score a hat trick in a single period and the first since Dick Gamble on March 2, 1952. … Suzuki extended his multipoint streak to four games (two goals, eight assists). … Canadiens defenseman Jordan Harris had an assist and was plus-3 in 17:45 of ice time after missing eight games with a lower-body injury. … Columbus forward Mathieu Olivier (lower body) and defenseman Erik Gudbranson (upper body) did not play after each sustained an injury on Friday. ... Larsen did not have an update on Merzlikins after the game.