Brendan Gallagher had a goal and two assists, including one on Artturi Lehkonen's goal at 7:30 of the third period to put Montreal ahead for the third time, 4-3.
Gallagher gave the Canadiens their first two-goal lead of the season when he made it 5-3 at 11:56.
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"We talked after 40 minutes that we just want to continue what we were doing," Gallagher said. "We were having success playing that certain way, nothing needed to change. Even when we got up, it was the same way. You know, obviously [Lehkonen] scores the big goal, but we just wanted to keep playing the same way, keep doing the same things, and I think we got rewarded for it tonight."
Max Domi scored into an empty net to make it 6-3 at 17:32.
Carey Price made 26 saves for Montreal (2-1-2), which had lost two games in a row.
Jonathan Drouin had a goal and an assist to extend his season-opening point streak to five games (two goals, four assists).
"We know who we were playing," Drouin said. "We were playing a team that's won the Stanley Cup, that's won a lot of battles in the past, and they know how to win. So if we didn't bring it to them, they were going to bring it to us and they're probably going to get that win. So we wanted to be the first team to get after this third period and make sure we were controlling the pace."