Taylor Hall scored his second goal of the game at 2:53 of overtime for Boston (33-15-7), which has 73 points with one game remaining and will face the Washington Capitals in the first round of the Stanley Cup Playoffs.
Tuukka Rask made 16 saves for the Bruins, who are 6-1-1 in their past eight games and bounced back from the lone regulation loss in the stretch (5-4 to the New York Rangers on Saturday).
"I liked our game tonight," Boston coach Bruce Cassidy said. "I thought we were good in all areas. Certainly, pockets could be better, but I thought in general we played a sound game, solid game. Much better defensively throughout. … It never got away from us. I thought we kept pushing. We wanted to win the game, wanted to play well, and hopefully stay healthy."
The Islanders (32-17-7) finished fourth in the East with 71 points and will play the Pittsburgh Penguins in the first round. Semyon Varlamov made 25 saves but did not play in the third period for precautionary reasons after he sustained "a little strain," according to coach Barry Trotz. Ilya Sorokin made 10 saves.
Trotz said he thought the game will help prepare New York for the playoffs.
"It's not always going to go your way, so you've got to battle through the situation," he said. "I thought we did and we got stabilized, and I thought our second and third periods were pretty darn good."
Hall won it for the Bruins when he slid the puck between the skates of Islanders defenseman Nick Leddy in the left face-off circle and scored on a backhand.
He gave Boston a 1-0 lead during a 5-on-3 power play at 19:21 of the first period.
Hall finished the regular season with eight goals in 16 games for the Bruins after he was traded by the Buffalo Sabres on April 12. Hall scored two goals in 37 games for the Sabres.
"It's obviously been a really good transition for me," Hall said. "I always felt like, even when I wasn't on this team, I felt like that was a style of play that I could come and play well in and perform well, and I feel like I've had a positive impact and it's important for me, just personally, to try and maintain that impact in the playoffs."