David Pastrnak scored twice, and Charlie McAvoy had three assists for the Bruins, the No. 3 seed. Tuukka Rask allowed four goals on 16 shots and was pulled after the second period. Jeremy Swayman made two saves in the third.
Game 6 is at New York on Wednesday (7:30 p.m. ET; NBCSN, SN360, TVAS). Teams that win Game 5 after a 2-2 tie are 215-58 (78.8 percent) winning a best-of-7 NHL playoff series.
"We'll be ready to go. No doubt in my mind we'll be ready to go," Bruins coach Bruce Cassidy said. "We were, I thought, the better team tonight. It didn't show on the scoreboard.
"Again, we've got to fix some things. Obviously, our [penalty kill]. [Brandon] Carlo and [Kevan] Miller (two injured defensemen) eat up a lot of those minutes. We miss them back there. We had some breakdowns we need to correct. Guys don't have their abilities on it, but we've got to coach them up, make sure they're better. That's what's in front of us that sticks out right now. Obviously, some 5-on-5 things, but I thought 5-on-5 we were dominant. But the PK let us down and we've got to get better at it."
Boston trailed by three early in the third period, but Pastrnak scored a power-play goal at 3:48 to make it 5-3, and David Krejci's rebound attempt trickled over the goal line at 14:43 to make it 5-4.
The Bruins outshot the Islanders 18-3 in the third. New York used its timeout after Krejci's goal.
"I wish we would've had five, 10 more minutes to tie it," Pastrnak said. "It's frustrating, but you know, we've got to let it go and the main focus is to get ready for Game 6. I think we've been the better team, but it just didn't go our way today. So just let it go and refocus."
Pastrnak gave the Bruins a 1-0 lead 1:25 into the first period on a one-timer from McAvoy.