The Islanders have won 12 of 17 games following the All-Star break.
"They're all big games," Islanders coach Jack Capuano said. "This group believes in each other."
"[It's] so much more fun, winning," Montoya said.
Nathan Horton and Zdeno Chara scored for the Bruins. Chara, booed every time he touched the puck, was playing his second game since his devastating check to Max Pacioretty that sent the Montreal left wing to the hospital with a severe concussion and non-displaced fracture of the fourth vertebrae Tuesday night.
"Every time I got booed, I got cheered by Boston fans. So I'm kind of used to it," Chara said. "It doesn't bother me. It's part of the game. Fans have the right to express opinions toward different players. It's part of the game, part of hockey. Fans have the right to cheer for the home team and against the visiting."
Horton opened the scoring with 3:31 left in the first period with his 20th goal. Milan Lucic took a pass from behind the net from David Krejci. Lucic held on to the puck until Horton was able to drive to the front of the net. Horton backhanded Lucic's feed past Montoya to the stick-side.
Horton has 13 goals and 25 points in 24 games against New York.
"It was a rebound. Obviously, Loouch tried to put it on net and it came right to me," Horton said.
Chara made it 2-0 with a power-play slap shot with 6:58 left in the second period. The goal was the Bruins' first with the man advantage since a 4-2 victory in Ottawa on Feb. 18.
"We also hit a couple bars on the power play," Bruins coach Claude Julien said. "Again, it's fighting it and get the confidence in our power play going again. With a little bit of luck, we could have had three goals. We just have to find our game again. We've been off our game. We seem a little out of sync right now."
Moulson's power-play goal with 2 seconds left in the second cut it to 2-1. Moulson one-timed a shot from just inside the right faceoff circle that Tim Thomas had no chance to stop.
Grabner tied it 1:28 into the third period with his 28th of the season. Kyle Okposo tied up three Bruins in front of Thomas before shoveling a pass to Grabner, who whipped a shot just past the outstretched stick of Chara and into the net.
"Huge goal for us," Hillen said.
Hillen scored on a slap to give the Islanders the lead at 5:58 of the third.
"I didn't want to pass up on any shot," Hillen said.
Boston has lost four in a row for the first time all season. ... The Bruins are third in the Eastern Conference. ... Thomas stopped 38 shots.