It only seemed to be the other way around in the opening two games of their NHL Eastern Conference semifinal, which the two teams split even though the Bruins had a wide advantage in puck possession and pressure.
The Canadiens have their power play, which went 4-for-9, and strong play from goalie from Carey Price to thank for having their best-of-seven series tied 1-1 going into home games Tuesday and Thursday at their 21,273-seat arena.
The Bruins have dominated at even strength, outscoring Montreal 8-3.
"The first thing is, when they come into our zone, we have to do a better job of getting on the puck first, being quicker," defenceman Josh Gorges said Sunday on a conference call. "Even if they get to the puck, we've got to try to stop their cycle, eliminate it right away and get the puck moving.
"We've got to spend more time down in their end. Wear them down, so when they get the puck out, they're not fresh and able to play in our end as much."
Despite the troubles in clearing their zone, the Canadiens won the series opener 4-3 in double overtime after blowing a 2-0 lead.
They wasted a 3-1 advantage as the Bruins scored four times in the last 9:04 of the third period for a 5-3 win in Game 2 on Saturday afternoon.
For fans of obscure statistics, it was the first time the Bruins ever won a playoff game in regulation time after overcoming a two-goal deficit in the third period.
Blowing leads is epidemic in this year's post-season. On the same night, Anaheim gave up a goal in the dying seconds of regulation and then lost in overtime to Los Angeles. Eleven of the first 53 playoff games this year have seem teams come back from two or more goals to win, compared to only eight in all of last year's post-season.
"It just shows that all teams are competitive and want to win and that no team will give up," said Gorges. "Everyone knows the importance of winning these games and that no lead is ever safe and no team ever quits. Boston didn't give up. They kept coming.
"Moving forward, the biggest thing for us is to not stop playing our game. We can't sit back and try to protect a lead. We have to keep pushing forward and be aggressive and keep playing our game."
Coach Michel Therrien doesn't think sitting on the lead was the problem. He pointed out that the Canadiens had allowed only one shot on goal in the first 10 minutes of the third period.
"We had good puck pressure, we were in full control," Therrien said. "But it takes breaks to win.
"Look at the (Patrice) Bergeron goal. The puck took a funny hop in front of the net and went over Carey's shoulder. I thought we were not a team that was playing on their heels."
On home ice, Therrien will have the last line change. That might help keep the NHL's first-place overall team somewhat at bay.
It should allow the Canadiens to keep their top line away from Bruins defence anchor Zdeno Chara, who was plus-five in Game 2, and get better line match-ups.
Therrien avoided questions on how he may use the advantage, but said the team will start making adjustments in practice on Monday that will be used in the next game.
He was upbeat despite the blown lead, saying that if they had been offered before the series started to come home from Boston tied 1-1 they would gladly have taken it.
"We went to play two games where it's tough for any team to play in the NHL and we're out of there with the series tied," said Therrien. "That's the big picture.
"I think it's a boost of confidence for our players that we're able to compete with that team and play with that team. And one thing for sure, playing at the Bell Centre, with the fans and support we've got, is a tough place for the other team to play. I'm sure the players will feed off our fans."
Playing in Montreal is always a challenge for the Bruins, who tend to see red, white and blue conspiracies everywhere. The Canadiens cannot literally tilt the ice, although the Bruins wouldn't put it past them to try.
Even in Game 2, Boston coach Claude Julien felt his team got a raw deal from the officials and took an unsportsmanlike conduct penalty at the end of the second period for using bad language with them.
The refs gave Montreal six power plays to Boston's three, although the Bruins had a two-man advantage for more than a minute in the first period and failed to score.
After going 6-for-16 against Detroit in the first round, Boston is 0-for-5 on the power play.
But the Bruins can bring with them the momentum they built in the third period. And goalie Tuukka Rask broke the ice by finally winning a playoff game against Montreal.
Montreal is boosted by seeing right-winger Tomas Vanek score a pair of goals after being temporarily bumped to the fourth line for spotty play in the opener; and by rearguard P.K. Subban's four points in the first two games.
Therrien would not discuss any potential lineup changes.
He said winger Brandon Prust, who looks to be struggling, is "totally healthy."
Prust played fewer than nine minutes, largely because Therrien liked what he saw from rookie winger Michael Bournival, who returned to the lineup after sitting out a game in favour of veteran Travis Moen.
"He had a really good first round," said Therrien, who used Bournival in every game of an opening round sweep of the Tampa Bay Lightning. "We put him back in the lineup. I wanted to use his speed. I thought he did a good job with (Tomas) Plekanec."
He also hopes that popular singer Ginette Reno would be back to sing the Canadian anthem in Game 3. The Canadiens scored early after she had the crowd roaring in both home games against the Lightning.
"We'd welcome her with open arms," he said.