Marchand scored a breakaway goal with 1:15 left in the first. His 26th goal this season extended his goal-scoring streak to five games (six goals); he has scored in 11 of his past 12 games.
"Any chance he gets, he buries nowadays," Julien said of Marchand, who also had two assists.
Winnipeg had the first 12 shots of the second period before Boston followed with 14 consecutive shots. The Bruins had 27 of the game's next 29 shots and the Jets went more than 17 minutes without a shot.
"It was a character win, but if you look at the way we played in the first 30 minutes, you're not going to win [many] games if you play like that," Rask said. "But it was a character win, we battled back and stuck with it."
After a scoreless second, Pastrnak's sixth goal this season 35 seconds into the third period extended Boston's lead to 4-2. Pastrnak skated down the right side, attempted a shot and put in his own rebound past Hutchinson's left pad.