Boynton beat Nikolai Khabibulin with a wrist shot from the slot for his second goal of the season and extended the Bruins' unbeaten streak at home to nine games.
Defenseman Bryan Berard tied the game with less than eight minutes left in the third period, flipping the puck through traffic past a screened Khabibulin.
Glen Murray put the Bruins on the board 3:40 into the second period, tying Atlanta's Ilya Kovalchuk for the league lead with 17 goals. Murray also scored twice at Atlanta on Thursday night, including the game-winner with less than two minutes remaining in overtime.
The Lightning are winless at Boston in 17 games, with the last victory coming on April 9, 1994. Boston is 7
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