Hall gave Boston a 1-0 lead at 17:26 of the first period when his wrist shot from a sharp angle along the goal line found its way past Sorokin.
Boston outshot New York 13-6 in the first.
"We were the better team in the first period; they're at home and obviously have got a lot of pride," Bruins coach Bruce Cassidy said. "What happens a lot is if the home team doesn't have a good first period, usually they'll push in the second. We've addressed that. It happens to us a lot. … We've just got to be ready for it and execute. You've got to be able to execute at a level to sort of stem the pushes that they have."
Jean-Gabriel Pageau tied it 1-1 at 11:30 of the second period, getting the rebound of Dobson's one-timer on the power play.
Sorokin prevented the Bruins from regaining the lead less than a minute later with back-to-back pad saves against Brandon Carlo and Hall, who also hit the crossbar from the left circle at 18:47.
"'Soroky,' the first goal he'd probably want back, but he made some big saves, key saves when it was still 1-1," Islanders coach Barry Trotz said. "From that, we just got confidence. He's such a good goaltender. We're fortunate we have two good goaltenders (also Semyon Varlamov), and we responded.
"You get energy from the big save, you get energy from a big special teams stop or a goal, and we stuck with it. We stuck with it right until the end."