Mathew Barzal, Josh Bailey and Jordan Eberle each had a goal and an assist for the Islanders, the No. 4 seed in the MassMutual East Division. Semyon Varlamov made 40 saves to help New York take the lead in the best-of-7 series.
The Islanders finished 3-for-4 with the man-advantage and are 9-for-31 (29.0 percent) in 11 Stanley Cup Playoff games.
"I feel like our power play's been pretty consistent through these playoffs," Barzal said. "It's helped us in a lot of games, whether it's taking the lead or getting us back in the games, so we're just trying to take what's there. Obviously, Boston's got a great PK, and so did [the] Pittsburgh [Penguins] (in the first round). It's just a matter of bearing down on your chances and then shoot when you get a lane."
Video: NYI@BOS, Gm5: Eberle wires home PPG from the circle
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.
Video: NYI@BOS, Gm5: Pastrnak opens scoring with one-timer
Barzal scored for a third straight game and tied it 1-1 on the power play at 18:49 with a wrist shot from the right face-off circle.
"That was key," Barzal said. "Obviously we probably didn't deserve to have the game at 1-1; they came out pressing, they probably could've had three or four in the first period. Just to get that tied 1-1, take a deep breath, just recoup for the second … obviously the power play was huge tonight."
Kyle Palmieri gave New York a 2-1 lead with a power-play goal at 4:49 of the second period. He scored on a tap-in near the left post after Bailey's attempted feed hit the skate of Bruins defenseman Connor Clifton in front.
Marchand tied it 2-2 when he powered his way around Islanders defenseman Ryan Pulock and stuffed a shot past Varlamov at 7:27.
Video: NYI@BOS, Gm5: Marchand dekes and scores gorgeous goal
Varlamov kept it tied later in the second with saves against Patrice Bergeron (on a rebound at 9:44) and Taylor Hall (one-timer at 11:24).
Bailey gave New York a 3-2 lead with a shot from between the circles at 14:30.
"I think 'Varly' did a good job weathering the storm for us," Bailey said. "We just had to hang in there. I thought we turned the game around as it went on, and then late, they've got a good team. They pushed hard, the crowd was into it. Ultimately, we found a way to get the win and give ourselves an opportunity here back at home."
Eberle scored the Islanders' third power-play goal at 16:38 to make it 4-2.
Rask allowed three goals on nine shots in the second. It was the second time he was pulled in 103 playoff starts.
"There was maintenance that needed to be done," Cassidy said. "He wasn't 100 percent, so we made a decision. That's the call we had to make between periods. Let's just say he wasn't himself, 100 percent. Certainly, he could've went back in. We made a decision not to put him back in."
Video: NYI@BOS, Gm5: Bailey finishes feed from Pageau
Brock Nelson gave the Islanders a 5-2 lead at 1:59 of the third period.
NOTES: The other time Rask was pulled in the playoffs was Game 5 of the 2018 Eastern Conference First Round against the Toronto Maple Leafs when he allowed four goals on 13 shots in 31:55 in a 4-3 loss. … Bruins center Curtis Lazar left the game in the first minute of the second period because of a lower-body injury. There was no update. … Carlo missed his second straight game, and Miller has been out the past six, each with an undisclosed injury. … It was the first time the Islanders scored at least three power-play goals in a playoff game since April 23, 2002, when they scored four in a 6-1 win against the Maple Leafs in Game 3 of the Eastern Conference Quarterfinals. … Palmieri extended his point streak to four games (three goals, two assists). … Varlamov has allowed a goal on one of the first three shots he's faced in five of six starts this postseason. … New York forward Oliver Wahlstrom (lower body) missed his sixth consecutive game.
Video: Islanders defeat Bruins in Game 5, 5-4