With the game tied at 1 early in the third period, Joseph took a pass from Alex Killorn, made a move against Bruins goalie Tuukka Rask and slipped in his ninth goal in at 2:40.
Cirelli scored Tampa Bay's fourth short-handed goal of the season when he stole the puck, put a fake on Rask and potted his fifth goal at 4:03.
Boston's David Krejci scored with 1:45 remaining and the extra attacker on -- his first goal in 19 games -- but Tampa Bay held on for its season-high fifth consecutive win.
Brayden Point scored his team-best 21st goal for the Lightning, who earned their eighth victory in their last nine contests.
Louis Domingue made 33 saves in his return to the Tampa Bay net after having his NHL-high 11-game goalie-start streak end Tuesday in Detroit.
Rask recorded 27 saves.
Boston welcomed back top-pairing defenseman Charlie McAvoy, who was activated from injured reserve earlier in the day. McAvoy sustained a concussion on Oct. 18 against Edmonton and had appeared in just seven games all season.
Boston top-line center Colby Cave had a steal in the offensive zone and quickly put a shot on goal, and Pastrnak cleaned up the rebound for his 20th goal at 2:04. The goal was the third in the past 10 games for the right winger.
Point evened it at 14:59 in a mad scramble in front of Rask after Nikita Kucherov whipped a pass into the slot to the high-scoring center. Tyler Johnson also assisted on the marker.
Boston played a tighter game in the second period and led 12-6 in shots over the Lightning, but neither club could break the tie.
--Field Level Media
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