Marchand and Jake DeBrusk scored for the Bruins, who opened a nine-point cushion over second-place Tampa Bay with 15 games remaining. Marchand, who has points in 10 consecutive games, played a season-low 14:36 after a bout with food poisoning in the morning.
Tukka Rask made 20 saves for Boston, which has won three straight and eight of 10, allowing one goal in the past two games.
''The further the season goes and as you get into the playoffs, you're going to need that solid team defense,'' Rask said. ''In the playoffs you're not going to win 6-5 or 5-4, it's going to be tight-scoring games. I think we've gotten used to that this year.''
Mitchell Stephens scored for Tampa Bay, which has lost five of the past six in regulation. Andrei Vasilevskiy stopped 33 shots.
''They play hard, they play a really good defensive game and that's why they are one of the top teams in the league,'' Stephens said. ''We have a good team in this locker room and we just need to regroup.''
The Bruins took advantage of an icing call to grab the lead late in the first period as Boston coach Bruce Cassidy was able to get his top line out against Tampa Bay's fourth line. Patrice Bergeron won the faceoff from Cedric Paquette and 18 seconds later Torey Krug found Marchand cutting through the left circle with a step on Mikhail Sergachev. Marchand had the puck go off his skate and past Vasilevskiy with 54.7 seconds left in the period.
''That's the exact play we wanted,'' Krug said. ''I wanted that puck to land on his stick and luckily it hit his skate. It was good movement overall.''
Tampa Bay thought it tied the game at 5:21 of the second on Yanni Gourde's one-timer, but Cassidy challenged for offside. The replay showed Tyler Johnson was a fraction ahead of the play, and the goal was overturned.
The Bruins took a two-goal lead 4:34 later as Gourde sent a pass back to the point that was deflected out of the zone. DeBrusk shook off Zach Bogosian's swipe check that tripped him up before regaining his balance and finishing off the play for his 19th goal of the season, first since Feb. 8.
''Anytime it goes in the net it's always a nice feeling,'' DeBrusk said. ''I haven't seen that in a while. It was nice, the play overall. That's what I want to be ... use my speed and effort. It's just nice to contribute at that time of the game.''
The Lightning cut into the lead with 2:32 left in the second. Stephens was parked on top of the crease to clear a path for Johnson before wheeling around and firing a rebound past Rask for his third of the season.
Rask kept Boston in front, denying Anthony Cirelli on a breakaway at 5:06 of the third. It was one of 22 shot attempts in the period, though only seven were on goal.
''We got a little more aggressive in our game, we changed our attitude, shot the puck a little bit more,'' Lightning defenseman Victor Hedman said.
NOTES: Marchand was sick early in the day and missed the morning skate. ... DeBrusk appeared in his 200th career game. . Injured defensemen Ryan McDonagh (lower body) and Jan Rutta (lower body) took part in Tuesday's optional morning skate for the Lightning. Both have been out since the first week of February. . Tampa Bay RW Nikita Kucherov was held without a point for the first time since Jan. 12, though he missed a game due to injury on Feb. 13. His seven-game scoring streak came to an end.
Bruins: At the Florida Panthers on Thursday.
Lightning: Host the Montreal Canadiens on Thursday.
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