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ST. LOUIS — In the lead-up to the Bruins’ staving off Stanley Cup extinction, coach Bruce Cassidy preached that his team could win without its first line of Patrice Bergeron, Brad Marchand, and David Pastrnak producing points. Fortunately for Cassidy and the Bruins, they didn’t have to test that theory. The Bruins might have been able to win Game 6 without contribution from their top line, but they didn’t have to.

On Friday, Cassidy hedged his bets on his top line, stating he believed the Bruins could prevail without it producing. But he also acknowledged “we could use a big goal from them” and “usually your best players at some point have to come through.” They did.

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They all contributed to a season-saving 5-1 win Sunday at Enterprise Center that silenced St. Louis Blues fans and a city that had been waiting for exultation and the appearance of the Stanley Cup, which is shipping up to Boston for a decisive Game 7 Wednesday. Hockey season in Boston is extended, and so is this series of Hard Rock and hard-luck hockey. Secondary scoring is nice and necessary, but being able to rely on your hockey headliners when it matters most is part of the DNA of championship teams.

The Bruins’ big guns got the job done. Brad Marchand (a goal and an assist) opened the scoring by whistling a five-on-three power-play strike past Blues goalie Jordan Binnington at 8:40 of the first period. David Pastrnak, who entered the game a team-worst minus-5 in the series, extinguished any hopes of a St. Louis comeback with a brilliant finish for Boston’s fourth goal at 14:06 of the third. You won’t find Patrice Bergeron’s name on the score sheet, but the classy conscience of the franchise made perhaps the biggest contribution of all: an impassioned speech that got his teammates going.

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What is it about St. Louis that brings out inspirational oration from Boston athletes? Six years ago, about a half mile away at Busch Stadium, former Red Sox slugger David Ortiz delivered a dugout address before the sixth inning of Game 4 of the 2013 World Series against the St. Louis Cardinals, spurring the Sox to victory.

“Obviously, it’s unbelievable leadership,” said Pastrnak, who finished with a goal and an assist. “It’s insane what these guys can bring to the team every single day and every practice. Obviously, sharing moments like he did, it’s inspirational and it’s touching for every single guy. Obviously, it got us going.”

Moments like this and performances like this are why it would be a shame if Lord Stanley’s chalice slipped through the Bruins’ grasp. This is a team deserving of carting the Cup around the ice. It’s a team with determination, heart, and resolve, starting with its Big Three forwards.

The Bruins were really good and a little lucky in Game 6. It started with their best players getting them off on the right foot. There was no playing of the Blues’ insipid victory anthem, “Gloria.” To paraphrase a lyric from the song, the Bruins had the Blues’ number, and it was five-on-three.

With 58 seconds left on the Bruins’ first power play, Blues series hero Ryan O’Reilly sent the puck over the glass while trying to clear it. That was enough to reignite the Bruins’ dormant power play. Just 21 seconds later, Marchand announced his presence.

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It was a good omen. The Bruins entered the game 24-1 all-time in the postseason — including 7-0 this postseason — when Marchand has scored. The Blues were doomed.

The Bruins’ 1-0 lead subdued a St. Louis crowd yearning for the Cup and yearning to exorcise 50-plus years of demons. Tuukka Rask (28 saves) took care of the rest, until Binnington cracked, turning into a human colander. He allowed a bouncing-puck goal to Brandon Carlo just 2:31 into the third period that doubled Boston’s advantage.

Maybe it was the Hockey Gods balancing the scales from the egregious noncall that created St. Louis’s second goal in Game 5.

Marchand, who had the primary helper on Pastrnak’s nifty goal, now has seven goals and nine assists in 16 elimination games. He’s 3-2—5 in elimination games this postseason. He’s the Julian Edelman of the Bruins, a little guy who finds a way to be clutch when it matters most.

You have to love the Little Ball of Hate. He backs up his bravado.

“I think it’s always been who he is, his makeup, the way he plays the game,” said Bergeron. “He’s always got that edge, and that’s when he’s at his best. He always steps up in big moments because of that energy that he brings, and the edge that he always wants to get that puck.”

Pretty much all of it went Boston’s way during this evening on the edge. Rask, with an assist from Charlie McAvoy, made a behind-the-back save of a puck that hit the post and went behind him in the second period. Carlo’s throwaway shot in the third bounced for Boston, breaking the back of Binnington and the hearts of the Blues faithful. Cassidy inserted Karson Kuhlman into the lineup, and Kuhlman scored his first playoff goal. Zdeno Chara, playing through a busted jaw, scored an empty-net goal.

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“Well, we’re fighting for our lives,” Marchand said. “When you play desperate, normally you see everyone’s best game. I think that’s what we had tonight.”

The Bruins’ best players helped extend their season. Now they have an opportunity to skate the Cup around Causeway Street, as the Spoked-B’s host a Game 7 of the Stanley Cup Final for the first time in the franchise’s storied history.

“The whole hockey world loves a Game 7,” said Cassidy. “It should be a great night in Boston, and may the best team win.”

Cassidy is clearly adopting a psychological approach of not putting pressure on his top guys. The Bruins faltered in the playoffs last year because they were too reliant on their top line. They didn’t have enough secondary scoring. They have it this time.

But it’s a complement to, not a replacement for, your best players being your best players.

“We believe this is the year that we’ve got secondary scoring,” said Cassidy. “That’s why we’re still playing. You need it in the playoffs.

“There are different guys that have to come through, and we’ve been able to do it. I hope [Bergeron, Marchand, and Pastrnak] come through for us, and they’re our best offensive players, on Wednesday. But I don’t want to put that pressure on them. Just play your game, and maybe tonight’s game will ease them a little bit into relaxing, and it will work for them.”

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The Bruins are the better team, especially when the members of the Perfection Line are clicking and contributing — whether it be with points, puck possession, or artful words.

But if they’re to be the best team in hockey this season, they’ll need more of what they got on Sunday night in St. Louis. Their best players delivering when it matters most.


Christopher L. Gasper can be reached at cgasper@globe.com. Follow him on Twitter @cgasper.