The Bruins turned up the offense with 15 third-period shots against Scott Clemmensen and pulled away to end a two-game skid. Florida has lost seven in a row and has managed just three victories in 16 games this season.
Boston held a 1-0 lead heading into the final period thanks to a David Krejci goal 7:17 into the second.
Marchand then slipped a wrist shot past Clemmensen 4:09 into the third, after which Torey Krug and Reilly Smith tallied for the Bruins.
Clemmensen finished with 27 saves.