TAMPA ­— As the puck crossed the goal line and tapped off the stick of Brad Marchand just 10 seconds into overtime, it felt both destined and improbable. It was the culmination of a stretch in which the Bruins had taken seven-of-eight points against the Blackhawks, Capitals, Panthers and, now, the Lightning, a run of success that did not seem likely when it began.

The Bruins managed two points against Florida on Monday, despite playing poorly defensively. They earned two points against Tampa Bay on Tuesday, despite starting backup goaltender Jonas Gustavsson and allowing the Lightning the first nine shots on goal in the third period at Amalie Arena.

But it was because of Gustavsson that the Bruins came out on top, winning 1-0 on a Marchand-from-Patrice Bergeron connection just after the opening faceoff in the extra session. The victory moved Boston into a tie with the Lightning with 83 points atop the Atlantic Division, though Tampa Bay has one game in hand.

Gustavsson played his best game of the season, stopping a career-high42 shots from the Lightning, and earning his first shutout of the year.

“He was outstanding, I thought, tonight,’’ coach Claude Julien said. “That big save with the pad in the second period. But even other saves, he was big. They had to be good to beat him tonight, and that’s a huge boost for our team when you can put a goaltender like that in a big game and play the way he did.’’

It was even more impressive, given that Gustavsson hadn’t played since Feb. 22, a span of seven consecutive starts for Tuukka Rask. Gustavsson’s last start had not been a particularly good one. He allowed five goals to the Blue Jackets.

Before the Bruins left Boston, Julien told him that he was the possible starter on Tuesday. So he prepared with that in mind. And whatever he did worked.

“To his credit, he works so hard and he tries to keep himself sharp,’’ Julien said. “It’s nice to see a guy like that being rewarded with a showing like he had tonight.’’

Perhaps none of his saves was bigger than a pad he got on a shot by Alex Killorn at 8:30 of the second, from Ryan Callahan. The crowd reacted as if Killorn had scored. He hadn’t, just barely.

No one else would beat Gustavsson.

“He played incredible,’’ Marchand said. “We wouldn’t have won if he didn’t play the way he did. He made a few huge saves, especially late in the game, really kept us in it. This one is definitely all him.’’

Gustavsson wasn’t left out to dry quite as badly as Rask had been on Monday night, when he needed to make 47 saves for the win. The Bruins tightened up a bit against the Lightning, keeping them to more shots from the outside.

“I think we have to be happy – it shows that we’re learning how to win these games,’’ Marchand said. “[Monday night] wasn’t our best game, but to bounce back the way we did tonight and play tight defensively, get the two points, is huge. To be able to win these games coming down the stretch like this is big.’’

It was far from perfect, though, with the Bruins being outshot in the second period by a 19-11 margin and spending a less-than-optimal amount of time in the offensive zone. Of course, the Bruins also didn’t have any power plays in the game. The Lightning had four, which did help with the shot disparity.

“We wanted to bounce back from last night, especially defensively,’’ Bergeron said. “I thought we did that. Obviously we gave them a lot of shots, but a lot of them from the outside and we found a way. At this time of the year, that’s what you want, especially against teams like we’ve been playing.’’

Before the game, Julien had said that he was worried more about the Bruins righting their play than about earning two points. He had been disappointed Monday, even with the win, and he needed to see a correction. He did.

And with that correction, the Bruins put themselves into a good position. They have gone 7-2-1 in their last 10, and have gotten 9-of-10 points since the trade deadline.

“Now we are playing good hockey,’’ Marchand said, adding that they had needed time to grow and integrate new faces. “We’re not playing our best every night, but we’re playing well enough to win. We’ve had a few really good games. That’s what we need right now. We’re playing the way we should be and we have to continue to do that.’’

Amalie Benjamin can be reached at abenjamin@globe.com. Follow her on Twitter @amaliebenjamin.