The Bruins trailed 2-0 after the first period, but used a power-play goal from Tyler Seguin and an even-strength marker from Rich Peverley in the middle frame to forge a 2-2 tie.
The Lightning's Brendan Mikkelson then drew a double-minor for high-sticking with 5:39 remaining in the third, and Marchand made Tampa Bay pay by beating Mathieu Garon during a 2-on-1 break with Patrice Bergeron.
Anton Khodobin made 20 saves for Boston, which reeled off its sixth straight victory.
Steven Stamkos scored his NHL-best 15th goal and Alex Killorn also found the net for the Bolts, who dropped their fourth straight and fifth in six contests.
Garon finished with 24 saves.
Swim Week Miami Beach 2014 [PHOTOS]