They had four chances to do it last year against Philadelphia and failed each time, eventually falling in seven games after taking a 3-0 lead in the series.
So they won't be taking any solace in the fact that they have two cracks at eliminating the Canadiens this year after building a 3-2 series lead with a 2-1 double-overtime win in Game 5 on Saturday.
They want to end this Tuesday in Game 6 in Montreal. A loss would force a potential Game 7 back in Boston less than 24 hours later on Wednesday, leaving little time to regroup and stem Montreal's momentum from the previous night.
But the Bruins aren't worrying about a possible Game 7. Their focus is strictly on Tuesday's Game 6, and a victory in that one will make the issues of playing two high-intense, pressure-packed games in two nights a moot point.
"I guess as a team right now, we're not thinking about Game 7, we're thinking about Game 6," Bruins coach Claude Julien said after practice Monday at the Garden before the Bruins departed for Montreal. "And that is what is on our mind. That is what should be on our mind. And we realize how important it is to come play probably our best game of the series. And that's basically where our focus is right now.
"Just to talk about something else right now I don't think is the right approach," Julien added when asked if avoiding having to play on back-to-back nights made it more important to close out the series in Game 6. "It's also a waste of energy and time. We have to focus on the moment. And you hear a lot of coaches and you hear a lot of players talking about the moment, and that's what he have to focus on is the moment, and the moment is [Tuesday], us being ready to play Game 6."
Game 6 will be back in the Bell Centre, where the Bruins will again face a rabid crowd and a desperate Montreal club that is usually tough to beat on home ice. But the Bruins have been a better road team all season, and that has held true this series with Boston winning Games 3 and 4 in Montreal after dropping the first two at home.
"Well we know what the crowd is like, we know how good they are at home, we know how they come out with a lot of jump, and we understand that whole situation," Julien said. "And I think we've done a pretty good job of handling it in Games 3 and 4 and it's going to be even more important again to understand that and be ready for it. And as I mentioned earlier, it goes back again to what I said, our determination has got to be there because they're going to come out with some desperation. They're going to come out hard and we have to be ready for that and we got to be ready to push back."
The Bruins know all too well what happens if they don't push back. The Flyers showed them last year how quickly the complexion of a series can change. And this year Boston has even less margin of error to play with.
But the Bruins also insist they've learned from last year's disastrous finish, and aren't about to let another series get away from them.
"Every year, every playoffs, is different," Bruins captain Zdeno Chara said. "You see some similarities, teams coming back from being down 3-0, coming back to even the series. But every year is different, and we all know the importance of [Tuesday's game]. For sure, it's a huge game and we have to bring our best.
"It's back-to-back, so for sure it's important [to win Game 6]," Chara added. "It's not like you're saving anything for Game 7. You have to play all out in Game 6 just like any other game and work extremely hard and play for 60 [minutes]. You can't be going into Game 6 thinking I have to save something for the next day."