Boston dominated the first half of the second period but the Lightning managed to weather the storm and flip momentum. With the Bolts on a power play midway through the period, Stamkos was left wide open in the slot and scored after Nikita Kucherov made a nice play behind the Boston net to get him the puck.
The power play seemed to energize the Lightning, as they had several opportunities down the stretch of the period to take the lead but were stymed by Tuukka Rask.
The Bolts' power play struck again early in the third period to take the lead. Moments after Kucherov was robbed of a goal on a diving save, he made a no-look pass to Brayden Point who fired a shot over Rask's shoulder to put Tampa Bay in front.
With less than five minutes remaining, Stamkos scored his second goal of the game to stretch the lead to stretch the lead to two. Stamkos forced a turnover at the blueline and shielded the puck from Bergeron before firing the shot past Rask.
John Moore pulled Boston back within a goal late but that would be as close as the Bruins would get.
Vasilevskiy was stellar in goal for Tampa Bay on Thursday, making 27 saves, including some key stops as the Bruins tried to extend their lead early in the second period.