The Lightning battled Boston to a 2-2 tie through the first 30 minutes, but were blanked the rest of the way by Tuukka Rask.
Marchand's slap shot found the net with 6:02 left in the second period go give Boston the lead for good and Horton tacked on a goal on a tip-in 2:33 into the third. Horton also opened the scoring just 1:11 into the contest.
Rask made 24 saves to win for the eighth time in 11 appearances this season. Anders Lindback stopped 22-of-26 shots for the Lightning, who had won two straight.