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BOSTON  -- The Blues got their first-ever win in a Stanley Cup Final in their 14th try, beating the Bruins 3-2 on Wednesday night at TD Garden, and the win swung the series in their favor. Carl Gunnarsson scored the goal 3:51 into overtime on a shot from the blueline that found its way past Tuukka Rask.

The victory evened the series at a game apiece and gives the Blues home ice in the series, which continues on Saturday at Enterprise Center. The Blues are 8-3 on the road in the playoffs, compared to just 5-5 at home. The Blues have gotten at least a split in their first two games on the road in all four of their series.

Gunnarsson had almost scored in the third period, putting a shot off the post. In the break between the third period and overtime, Gunnarsson ran into coach Craig Berube in the locker room bathroom and told him he just needed one more chance.

"(Berube) just came in and said, 'Good job,' and told the story," captain Alex Pietrangelo said. "You don't hear that story very often. That's not a place to have a conversation, but I guess it works. It's a good story. I don't know if he's making it up because that's a great story.

"Just needed one more chance and he got it and he scored."

He got it, driving in a pass from Ryan O'Reilly. It was Gunnarsson's first career playoff goal.

"First game we weren't happy, today we came out flying," Gunnarsson said. "I think we played a great game for 60-plus minutes and that's just the team we are. We come back like that. We never give up. For me to put it in and get the winner, it's a great feeling."

"He just said he needed one more shot," Berube said. "He was joking around a little bit. But he played a hell of a game. He made a great shot.”

Gunnarsson had just three goals this season and has just 28 in his 10-year NHL career, so he's one of the last guys on the Blues -- maybe the last guy -- to make a prediction like that.

“I liked hearing it," Berube said. "He hit post. He had a hell of a game, I thought, and I’m really happy for him that he ended up getting that game-winner. He hit the post in the third there and he felt good about himself obviously, which he should have."

It's been a rough year for Gunnarsson, who played in only 25 games in the regular season because of injuries and who might not have played had Vince Dunn been ready to return to the lineup.

"It's a big spark," O'Reilly said. "It's a massive goal and he's a big piece of this team. He played an unbelievable game and to see that puck go in and see the celebration from him was inspiring for us all. It was incredible play by an incredible player."

"He got a second chance at it and made the most of it," Brayden Schenn said. "The boys are happy for him."

"He had his chances throughout the game," defenseman Joel Edmundson said. "Couldn't happen to a better guy. It’s a shot that all of us defensemen, we practice every pregame skate so it was nice to see that go in and it couldn’t happen to a better guy."

It also ended the franchise's record of futility. The Blues were 0-13 in Stanley Cup Final games going into Wednesday.

"It's one win," said forward Pat Maroon. "I guess it's exciting. But we've got to keep finding ways. Obviously it's history. They're I guess 0-13. We found a way to get a win. I'm sure every fan's been waiting for that victory for a long time and it's pretty exciting."

After taking the loss in Game 1, Jordan Binnington stopped 21 of 23 shots to continue his impressive streak of getting wins after losses. He stopped 15 shots in the second and third periods and didn't face any at all in the overtime.

“Life of a goaltender,' he said. "Just keep moving forward and regroup, just try to be there and give your team a chance to win. I keep that mindset.”

The Blues trailed twice in the first period and twice came back to pull even. Robert Bortuzzo and Vladimir Tarasenko, the omega and alpha of Blues offensive performers, each had a goal. Charlie Coyle and Joakim Nordstrom scored for Boston. Tarasenko's goal was his 10th of the postseason and he has a point in eight straight games.

It was the fourth overtime game for the Blues, who have one in each series. They lost to Winnipeg and San Jose (on the controversial hand pass) and won Game 7 of the Dallas series.

Through regulation, the Blues had 33 shots on goal and Boston 23.

In the third period, each team came close to scoring. Gunnarsson, one of only three Blues to appear in this postseason without a goal going into the game, put a shot off the post with just under two minutes to play. After that, Jordan Binnington made saves on dangerous shots by Brad Marchand and David Pastrnak. The Blues also had to kill off a dubious power play in the third when Brayden Schenn was called for slashing.

Neither team scored in the second period either, The Blues had a four-minute power play late in the period when Tyler Bozak took a high stick, but it was cut in half when Jaden Schwartz was called for goaltender interference. Boston had a power play early in the period that the Blues killed. The game got increasingly chippy in the second period, with plenty of action after the whistle. Tarasenko missed part of the second period, apparently with an equipment issue.

Coyle started the scoring after Sammy Blais was called for goalie interference. On the ensuring power play, Jake DeBrusk, trailing the play, got a pass and took the puck below the goal line, where he passed out front to Coyle, who was alone in the slot and shot between Jordan Binnington's legs to make it 1-0.

The Blues tied the game with 10:23 to go in the period on a shot by Bortuzzo that deflected in off of defenseman Matt Grzelcyk. The play was kept alive by Carl Gunnarsson racing to keep a puck in at the blue line.

Forty seconds later, Boston was ahead again. Sean Kuraly, who had the game-winning goal in Game 1, made a slick backhand pass from behind the net past two Blues to Joakim Nordstrom, who cut across the crease and backhanded in the shot, again between Binnington's legs.

With 5:05 to go, the Blues tied it again. Tarasenko played the puck out of the Blues' end to Jaden Schwartz on the left wing on a partial break. Schwartz's shot was blocked by Tuukka Rask, and the rebound came to Tarasenko. His initial shot was blocked by defenseman Zdeno Chara, but he got the puck again and reached out to put it past Rask.

Boston had a late power play after Oskar Sundqvist was called for boarding for crushing Grzelcyk into the boards. Grzelcyk was down on the ice and stayed down for a while before being helped off to the dressing room. The Blues killed the power play and Grzelcyk didn't return to the ice in the second period.

The Blues were playing without forward Robert Thomas, who had an undisclosed injury. Coach Craig Berube said it was not related to the hit he took in Game 1 from Boston's Torey Krug. Thomas has been nursing a minor injury, believed to be to his wrist, for two weeks, which has kept him from practicing but not from playing. 

Also not in the lineup on Wednesday was defenseman Vince Dunn, who missed his fifth consecutive game after taking a puck to the face in Game 3 of the San Jose series. Dunn has been more involved in practice and had returned to a regular visor from the full coverage one he had been wearing, but he apparently was not ready to return to action yet.

Game 3 is Saturday at Enterprise Center.

Tom Timmermann is a Blues beat writer for the St. Louis Post-Dispatch.