A Steven Stamkos power play goal tied the game at one late in the second period, but Taylor Hall's second goal of the night early in the third would go on to serve as the game-winner.
The Bolts now head to Philadelphia to wrap up the road trip against the Flyers on Thursday.
Scoring Summary
1st Period
BOS 1, TBL 0
1:07 Taylor Hall (7) - Brandon Carlo, Trent Fredric
The Lightning found themselves in an early hole when Taylor Hall put the hosts in front 1:07 into the contest. Hall got to the front of the net and redirected Brandon Carlo's point shot past Vasilevskiy for the game-opening tally.
2nd Period
BOS 1, TBL 1
18:20 Steven Stamkos (13) - Nikita Kucherov, Brayden Point - PPG
Career point No. 999 from Steven Stamkos tied the game at one late in the second period. On Tampa Bay's second power play of the night, Nikita Kucherov threaded a pass through the middle of the ice to Stamkos at the left circle and his shot beat Jeremy Swayman to draw the Bolts level.
3rd Period
BOS 2, TBL 1
2:49 Taylor Hall (8) - Nick Foligno, Hampus Lindholm - PPG
In the closing seconds of a Boston power play, Nick Foligno had the puck in front of the net but was forced to stickhandle down low. He then slipped a pass back to the slot for Hall to fire home and give the Bruins the lead again.
BOS 3, TBL 1
19:19 Brad Marchand (7) - David Krejci - ENG
Brad Marchand iced the game for Boston with an empty net goal in the final minute of regulation.