It wasn't long before Boston answered back with another power play strike.
With Nate Thompson in the penalty box for tripping, right-winger David Pastrnak put a one-timer past Price to give the Bruins a 2-1 lead.
The tally came just 1:43 after the Weber goal.
Brad Marchand capped the scoring in the period, making the most of a Jeff Petry turnover down low to put Boston ahead 3-1 with 37 seconds remaining in the period.
That's the way things stood through 20 minutes of play.
The Bruins came out flying in the middle stanza.
After Pastrnak scored his second goal of the game just eight seconds into the period, Anders Bjork added another goal at the 1:10 mark to give Boston a 5-1 advantage.
That was the end of the night for Price, who was replaced by Keith Kinkaid in between the pipes.
Price surrendered five goals on 11 shots.
The Bruins didn't stop there. Pastrnak completed his hat trick at the 9:06 mark of the period, tipping a weak point shot past Kinkaid.
It was 6-1 after 40 minutes.
Charlie Coyle and Danton Heinen added goals for Boston in the final frame.
The Canadiens will be back in action on Thursday night against the New Jersey Devils at the Bell Centre.