Cal Clutterbuck scored twice for the Islanders (8-12-5), who have won three of five games since an 0-8-3 stretch. They have won two straight at their new arena after losing the first seven.
"The last little while, it's been make-or-break," Clutterbuck said. "(We) put ourselves in a tough spot. But I've said this like a million times, we're just trying to focus on the day in front of us, one day at a time. Things can get overwhelming if you get too high or too low, so it's one day at a time."
Mike Reilly scored for the Bruins (14-10-2), who have lost two straight after winning their previous two. Linus Ullmark made 25 saves.
"I have no issue with the effort," Boston coach Bruce Cassidy said. "I thought our guys came to play tonight. I'd say after the first 10 minutes, we were on our toes much better. … All in all, I thought the guys played hard, tried to play the right way, got better as the game went on."
The Bruins played with 17 skaters (11 forwards, six defensemen) after seven players entered NHL COVID-19 protocol the past three days.
Center Patrice Bergeron was added to the protocol Wednesday, one day after forwards Brad Marchand and Craig Smith entered. Goalie Jeremy Swayman, and forwards Trent Frederic, Anton Blidh and Oskar Steen were placed in protocol Thursday.
"I'm always proud of this group," Boston forward Nick Foligno said. "That's the Bruin way. There's no quit in this team. With everything we've faced the past 24 hours, it's been a nightmare, to be honest with you. But we found a way to come in here and just work. That's something we can control.
"I think we also looked at it as an opportunity for some guys that don't get the same kind of ice time, and there's an opportunity in front of them. I thought some guys played real hard tonight and gave us everything they had."