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.