Pastrnak gave Boston a 3-1 lead at 2:13 of the second period, scoring on a rebound, and Marchand made it 4-1 1:43 later with a wrist shot from the slot.
Patrice Bergeron had an assist on Marchand's goal after missing four games because of an elbow injury.
"I think everyone is playing the right way and communicating," Bergeron said. "I've said it a few times, but I can see the growth in our team, the way that we're playing. Guys owning roles and playing the right way, doing it for the right reasons, obviously to win and help the team. It's great to see."
Lee cut it to 4-2 with a power-play goal at 5:12, putting in a rebound in front of the crease.
"I think it was a pretty solid hockey game for most of the start, even halfway through," Lee said. "They had some good pressure and made some good plays, got a couple bounces, and I think it just did get away from us a little bit. Against a good team like that it's tough to cover two or three goals."
Haula made it 5-2 at 14:33, and Jake DeBrusk scored at 18:18 to give the Bruins a 6-2 lead.
Zach Parise scored to make it 6-3 with a power-play goal at 14:43 of the third period.
NOTES: Bergeron played his 1,200th NHL game, joining Ray Bourque (1,518) and Johnny Bucyk (1,436) as the only players to do so with the Bruins. Chara played 911 games as Bergeron's teammate in Boston. … Nelson, 30, became the second Islanders player to have his first 30-goal season at age 30 or older (Jason Blake, 33 years old; 40 goals in 2006-07). … Bruins forward Nick Foligno left the game with an injury after a fight with Islanders forward Matt Martin at 13:10 of the third. There was no update on his status.