"I think first and foremost the win was the most important part of tonight's game," said Swayman, who made his fifth NHL start. "The shutout was kind of the cherry on top. I was just super excited to get that accomplishment and I know I'll remember that one for a long time. But again, it couldn't have been done without the defense I had in front of me, and the players up front as well. So I'm super happy with that team effort."
David Pastrnak and Curtis Lazar scored for Boston (24-12-6), which has won three games in a row.
Ilya Sorokin made 25 saves for New York (27-13-4), which lost 4-1 here Thursday and is 1-3-0 in its past four.
The Bruins lead the New York Rangers by six points for fourth place in the eight-team MassMutual East Division. The Islanders trail the Washington Capitals by two points for first place. The top four teams will qualify for the Stanley Cup Playoffs.
"It's not coming real easy right now," Islanders coach Barry Trotz said. "We played a really good hockey team that's I'll say desperate because they know they've still some ground to make and now they've got some games in hand. They're right with the four teams (atop the division) right now.
"We've got to just take care of our own game, but there's a lot of positive things to take out of this game. We were way better this game than we were (Thursday). If we had played this game the other night, I think we might have won the hockey game."