Winnipeg outshot Boston 13-7 in the first.
"[Swayman] was really important, especially in the first period when they outshot us pretty badly there," Zacha said. "He held us in the game, and our penalty kill too helped us a lot. There was a great team effort overall and we're happy to win."
Nosek scored an empty-net goal with six seconds left in the third period for the 3-0 final.
Swayman preserved the shutout with 12 saves in the third.
"A couple of goal posts, we missed a couple tap-ins around the net … yeah, it could've [gone either way]," Jets coach Rick Bowness said. "But we have to put those pucks in the back of the net. The opportunities were there. Their goalie was really good. We didn't capitalize on the chances they gave us."
Bruins defenseman Derek Forbort did not play in the third after he blocked a shot late in the second period.
Boston continues its five-game road trip (1-2-0) Saturday at the Minnesota Wild.
"I think we're going to get him evaluated tomorrow morning again just to see what exactly it is, but we know he's not going to be a player for probably the rest of this trip," Montgomery said.
NOTES:Swayman, 24, has eight shutouts in 75 career NHL starts. Frank Brimsek (16) and Tuukka Rask (11) are the only goalies in Bruins history with more before the age of 25. … Boston's 51 victories matches its win total from last season with 15 games still to play. … The Jets allowed a goal in the opening minute of the game for the third time this season and were shut out for the fourth time.