Charlie McAvoy, native of Long Beach, New York, had a goal and two assists for the Bruins (41-13-12), who haven't lost to the Islanders on the road since New York won 3-1 at the Coliseum on Nov. 2, 2013.
"He's a Long Island boy, so coming home he was probably a little more excited to play, and good for him," Bruins coach Bruce Cassidy said of McAvoy.
Boston leads the Atlantic Division by seven points over the Tampa Bay Lightning. The teams play Tuesday.
WATCH: [All Bruins vs. Islanders highlights]
Semyon Varlamov made 25 saves for New York (35-21-8), had their four-game point streak end (2-1-2) and failed to tie the Pittsburgh Penguins for third place in the Metropolitan Division.
The Islanders, who went 0-for-6 on the power play, were shut out for the third time in nine games and fifth time this season.
"When we had our looks, we didn't have second looks," New York forward Anders Lee said. "We did a great job of creating some initial shots; it's that second opportunity that we just didn't find tonight on some of the power plays, and then a couple of others we had nothing going. The ones we did have going, we just didn't have that secondary opportunity to put it in."
David Pastrnak's NHL-leading 47th goal gave the Bruins a 1-0 lead at 4:30 of the first period.