BOSTON -- They lost their best player way back in November. They were sellers at the trade deadline. Injuries have meant they don't have a single player who has played in all 72 games.

But the Tampa Bay Lightning, given up for dead more than once during this season, are still alive in the race for an Eastern Conference wild-card spot.

Having just lost three straight games at home, the Lightning fell behind three times Thursday night at TD Garden, tied the game all three times in under 1:36 and then scored three in the third to stun the fading Boston Bruins 6-3.

"It showed a lot of character," Anton Stralman said after his goal helped move the Lightning to just three points behind the Bruins, with a game in hand. "We didn't let it bother us. We kept playing strong and got rewarded"

It took the Lightning, who have been without Steven Stamkos since November, 44 seconds to answer the first Bruins goal, 24 seconds to answer the second and 1:35 the third.

Jonathan Drouin broke a 13-game scoring drought by beating Tuukka Rask with a slap shot 4:12 into the third period as Tampa Bay won for the first time in four games vs. Boston this season.

Nikita Kucherov followed with his second goal of the game and completed his third career hat trick (second this season) with his 37th goal of the season, into an empty net. Ondrej Palat picked up his third assist of the game on the goal.

"We have a young team right now and they're showing their character in the room," Kucherov said. "It's nice that we found a way to come back three times, and we closed this game out in the third, have to go to Detroit.

"We lost a lot of guys, and some other guys had to step up, and that's what we did in the third. Like I said, that shows character that we still have great guys and young guys in the room. That was nice today."

The Bruins, hoping to make the playoffs for the first time in three years, wound up getting booed off their own ice by the frustrated crowd.

"If we don't stop this on Saturday (against the Islanders in Brooklyn) then the bleeding really starts to get profuse," said Boston's David Backes, who had one of three Bruins penalties in the third period.

The Bruins lead the Islanders by two points, but New York, which plays in Pittsburgh on Friday night, has two games in hand.

Drouin added two assists, and Brayden Point and Anton Stralman also scored. Point added an assist and Victor Hedman had two assists.

Rask, strong at the start but shaky later on, finished with 23 saves.

Peter Budaj made 28 saves and raised his record to 5-1 at TD Garden. He lost to the Bruins twice earlier this season, once in Boston, while playing for the Los Angeles Kings. Budaj has two wins in three starts with his new team, both on the road.

David Pastrnak, Zdeno Chara and Riley Nash scored for the Bruins. Nash added an assist and Dominic Moore had two.

Lightning defenseman Jason Garrison had to be helped off the ice in the second period because of a lower-body injury; he did not return. Coach Jon Cooper said it "didn't look good" and said Garrison would be further evaluated on Friday.

After a scoreless first period, both teams scored three times in the second -- Pastrnak opening the scoring with his first goal in three games but his sixth in the last eight. But every time the Bruins ignited the crowd, the Lightning bounced back, as Rask turned shaky.

The Lightning scored four goals in a 12-shot span in the second and third periods.

"He's played a lot, but I don't have the answer, to be honest," said interim coach Bruce Cassidy, who is now living through the same problems that got Claude Julien fired. "He needed to be better tonight. We needed to be better in front of him, and he needed to be better on some of those goals."

NOTES: Lightning C Steven Stamkos still isn't sure he will make it back from knee surgery before the end of the season, but he's trying. "The knee is a tricky situation," he said after skating Thursday morning in Boston. "It's something I've never had to deal with before. It's all new to me." He hasn't played since Nov. 15. ... C Tyler Johnson, who suffered a lower-body injury on March 9, also remained out for Tampa Bay. ... The Lightning visit the Bruins again April 4. ... Zdeno Chara became the first Bruins defenseman with at least two short-handed goals in a season since Ray Bourque had two in 1995-96. ... The Lightning are at Detroit on Friday night.