TAMPA, Fla. -- When it gets 10 rounds deep into a shootout, the unlikeliest of heroes tend to emerge.

For Boston, that was Jimmy Hayes who converted his shootout attempt in the 10th round to give the Boston Bruins a 4-3 victory against the Tampa Bay Lightning on Thursday at Amalie Arena.

Hayes has struggled to start the season for the Bruins, failing to register a point in any game this season. Against Tampa Bay on Thursday, he had the second-lowest ice time of any Bruin, with only rookie Sean Kuraly -- who was making his NHL debut -- playing less.

Despite running out of available options, Boston head coach Claude Julien felt confident about tapping Hayes on the shoulder in the situation.

"You go down your bench and you look at who is next ... and at one point you have to go with your gut feeling," Julien said. "Jimmy is a pretty good shooter, he's one of those guys that can let the puck go, he has a quick release and at that point, I felt good about putting him out there. For some reason, I had a gut feeling he was going to do it and he didn't disappoint."

The Bruins picked up the victory despite blowing a pair of two-goal leads.

"You just try and take all the time and space you can away and keep them on the outside, but ... they're a very skilled team so they're going to get some chances," Rask said.

Brandon Carlo, David Pastrnak and Ryan Spooner scored for the Bruins while Tuukka Rask made 30 saves through regulation and overtime, allowing more than a goal for just the second time in six starts this season. Rask stopped 9-of-10 Lightning shooters in the shootout.

The Bruins have won three consecutive games, all on the road.

Tyler Johnson scored twice for the Lighting while defenseman Victor Hedman notched his second goal of the season for Tampa Bay. Andrei Vasilevskiy finished with 28 saves and stopped 8-of-10 attempts in the shootout.

Carlo opened the scoring just 4:01 into the game when the Boston defenseman skated with the puck from his spot at the right point and around the faceoff circle to put a bad-angle shot through a screen that eluded Vasilevskiy and dropped just inside the goal for a 1-0 lead.

Spooner one-timed a pass from Torey Krug past Vasilevskiy for a 2-0 lead at 10:47 on a power-play goal. Tampa Bay challenged the play for offside but review proved inconclusive on the back skate of Brad Marchand on the entry play.

"We have challenged three offside this year (losing twice) and to me I would challenge then a hundred out of a hundred times," Lightning head coach Jon Cooper said. "They are no doubt to me, but I'm only at 33.3 percent so I got to go look and see what offside is again."

Hedman pulled the Lightning to within one on a power-play goal at 15:09, one-timing a slap shot off a back pass from Nikita Kucherov.

Ondrej Palat appeared to pull Tampa Bay even early in the second period, but his goal was ruled to have been directed in to the net with a distinct kicking motion, keeping the Bruins in front.

Boston regained a two-goal lead when Patrice Bergeron sent a shot toward the net that deflected off Pastrnak at 4:38 before Johnson scored Tampa Bay's second power play goal of the game to cut the deficit to 3-2 at 8:30 of the second period.

Tampa Bay eventually caught the Bruins when Johnson notched his second goal of the game, getting his stick on a shot from Braydon Coburn to deflect the stick past Rask at 10:04 of the third period.

It's the third time in five home games Tampa Bay has fallen behind by two goals before rallying to gain at least a point.

"We had to battle ourselves out of it and we were able to do that," Johnson said. "It's just one of those things that we can't put ourselves in that hole every time."

NOTES: Lightning LW Jonathan Drouin was scratched with an undisclosed upper-body injury suffered in the first period of Tuesday's game against the New York Islanders when New York D Calvin de Haan delivered a blow to Drouin's head. ... D Nikita Nesterov was a healthy scratch for Tampa Bay for the second consecutive game. ... LW Matt Beleskey, who signed a five-year, $19 million contract as a free agent with the Bruins prior to the 2015-16 season, was a healthy scratch along with D Joe Morrow. ... Boston C David Backes missed his fifth consecutive game with an elbow injury. ... Bruins C Sean Kuraly made his NHL debut. ... Boston RW David Pastrnak returned to the lineup after serving a two-game suspension. ... Tampa Bay C Tyler Johnson recorded his 11th career multi-goal game. ... Lightning rookie C Brayden Point improved to 2-for-2 on shootout attempts this season. ... Tampa Bay recorded its fifth multi-power-play goal game of the season after converting 2-of-4 chances.