Rafael Harvey-Pinard put the Canadiens ahead 4-2 with a power-play goal at 18:41 of the second period. He got to the front of the net and deflected Mike Matheson's slap shot from the point.
Harris pushed it to 5-2 at 2:58 of the third, and Christian Dvorak scored short-handed at 9:12 for the 6-2 final.
Belzile, who was playing in his 20th NHL game, gave the Canadiens a 1-0 lead at 8:14 of the first period. He is the seventh-oldest player to score his first NHL goal for the Canadiens, and the oldest since Hockey Hall of Famer Herb Gardiner (35 years, 35 days) on Dec. 7, 1926.
"If we would have lost, the moment would be bittersweet," Belzile said. "But we faced a really good challenge tonight, and even yesterday with the comeback, that shows character. In the NHL, if you play as a unit of 18 plus the goalie, there is no easy game, and teams win over sometimes an individual, so we had a really good game."