Timo Meier scored, and James Reimer made 34 saves in his 11th straight start for the Sharks (23-23-6), who were held to a season-low 16 shots.
"We were bending a little bit in the first half of the game, but not breaking, which was good," Sharks coach Bob Boughner said. "We were giving ourselves a chance. There was a lot of shot volume against but there wasn't necessarily a bunch of high-end chances.
"The problem was we couldn't spend enough time in their end. We couldn't produce some possession time down there until the third period. [In the third] we kept battling, we kept working hard, and the guys played hard for one another. ... We had some chances at the end. I thought for sure we were going to get a bounce, but we didn't."
Marchand gave Boston a 1-0 lead at 14:24 of the first period after Jake DeBrusk's cross-ice pass set him up for a wrist shot from the right circle.
Meier tied it 1-1 at 12:50 of the second period with a one-timer on a power play.
"Sometimes it's tough when you're playing really well and you get a goal scored against you when we easily could've had four or five," Marchand said. "But just the composure of [our] group where earlier in the year maybe we would've folded. But we just kept going at it."
Marchand made it 2-1 at 3:18 of the third period. Taylor Hall sent a pass from behind the net and Marchand's shot bounced off Reimer's shoulder pad.
"When we get a lead in the third, it's still a work in progress for us," Bruins coach Bruce Cassidy said. "Like tonight, we probably made it more difficult than we should have. ... I don't think we managed it well in terms of going back with it to get fresh players on the ice, or when it did come into our end, around our net, or the breakout, whatever. Like I said, I think we could've made it easier on ourselves."