DeBrusk also had two goals and an assist in regulation, and Linus Ullmark stopped 23 shots for Boston, improving his record to 17-1. The Bruins are 15-0-1 at TD Garden, including the NHL-record 14 straight victories to open a season at home that was halted last week.
''They definitely took it to us that first period,'' Boston defenseman Derek Forbort said. ''Linus kind of held us in there. I thought we got pretty lucky that we got two goals out of it. We kept grinding and we found a way.''
Casey Cizikas, Josh Bailey and Noah Dobson each had a goal for the Islanders, and Semyon Varlamov made 30 saves before the shootout.
''We started the game, we find ourselves down two,'' Islanders coach Lane Lambert said. ''For us to climb back and go to the third being down, coming away with the point was a good job by our guys.''
After Pastrnak beat Varlamov under the crossbar, Ullmark dropped and stopped Bailey's bid to end it.
Coming off a 2-1 West Coast trip, the Bruins had jumped to a 2-0 edge when DeBrusk scored his two goals 19 seconds apart in the opening period before the Islanders rallied to tie it.
''This is the game it looked like we were set up to fail,'' Boston's first-year coach Jim Montgomery said of playing after a long trip. ''Everybody goes through it, there's a couple of games every year where it looks like you should have success and there's games where it looks like it's going to be a real battle. We were sluggish in the first, probably our worst period of the year.''
DeBrusk also set up Forbort's first career short-handed goal when he moved the puck quickly up the right wing and made a nice drop pass to Pavel Zacha, who centered it to a charging Forbort. The veteran defenseman fired a rising wrist shot that beat Varlamov into the upper right corner, pushing Boston ahead 3-2 late in the second.
But New York tied it again early in the third when Cizikas spun around the net and tucked the puck in off Ullmark's body.
''We know what we have to do to succeed,'' Cizikas said. ''We did a good job. We kept the puck in and we kept getting it to the net. ... Overall, we played a really good game.''
Boston center David Krejci missed his second straight game with a lower-body injury. ''If it was playoffs he'd be playing, but we're just making sure we're being cautionary,'' Montgomery said after the morning skate.
Islanders: Play the second game in a five-game trip on Friday at the Arizona Coyotes.
Bruins: Continue their five-game homestand Thursday night against the Los Angeles Kings.
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