"It's always nice to come home and sleep in your own bed after a win," Moulson said.
Josh Bailey and Moulson also had goals for the Islanders, who won for the second time in six games.
New York (27-29-9), which entered with the second-worst record in the Eastern Conference, had dropped the previous two meetings -- both in November -- to the Bruins. They lost 6-2 in Boston and 6-0 at home.
But Nabokov bounced back from allowing five goals on 29 shots in a 6-3 loss at Philadelphia on Thursday with a strong outing.
Tyler Seguin tied the game for Boston with his 22nd goal early in the third period. Milan Lucic also scored his 22nd, converting on a first-period power play.
The Bruins have dropped five of eight and hold a three-point lead over Ottawa atop the Northeast Division. Boston has played three fewer games.
Tim Thomas took the loss in relief of injured starter Tuukka Rask, who left the game with an undisclosed injury midway through the second period. Thomas stopped 11 of 13 shots after Rask gave up one goal on 12 shots.
More On The Bruins
Looking for more from the ice? Joe McDonald and ESPNBoston.com have you covered. Blog
Rask got hurt when he kicked out his left pad to try to stop a shot that went wide. He dropped to the ice in pain and was helped off by two players holding his arms as he skated off the ice. Thomas was already expected to start Sunday when the Bruins visit the New York Rangers.
Boston coach Claude Julien said Rask wouldn't make the trip, but elaborated little on the injury.
"It is what it is," he said. "You want to be able to use two goaltenders in this stretch, but it's not what it is."
The Bruins will play nine games in the next 16 days.
"It's obviously not great when you see him not able to get up after making an effort to make a save," Lucic said. "He's been a big part of our team this year."
After the game, the Bruins recalled goalie Michael Hutchinson and forward Lane MacDermid from Providence of the AHL.
The Islanders will play their next three games against New Jersey, beginning Sunday at home.
New York grabbed the late lead when Moulson fired a shot from the top of the right circle that was tipped by Tavares. The puck dipped and slid between Thomas' pads with 4:39 left.
The Bruins pulled Thomas for an extra skater with 1:20 to play, and Lucic had a good chance on a rebound during a scramble in the closing seconds.
"It sure looked like the bounces were definitely not on our side today," Lucic said. "For myself, it was a quick reaction. He got his paddle down, and I wasn't able to beat him."
Boston was held to two goals or fewer in eight of 13 games in February and was shut out five times. The Bruins rebounded with a 4-3 overtime win over New Jersey on Thursday -- the first day of March -- but were shut down again by the Islanders until Seguin tied the game at 2 at 7:29 of the third.
Boston D Andrew Ference didn't play because of an undisclosed lower body injury sustained Thursday against New Jersey. D Johnny Boychuk returned after missing two games with a concussion. ... Bruins D Mike Mottau, acquired from the Islanders on Monday, was a healthy scratch. ... New York had given up 14 goals in its previous three games, all losses. ... MacDonald said after the game that Lucic grabbed his chin strap in a scrum and "threw it in the stands." Moulson was laughing in the background when he heard him tell the story. ... Boston F Daniel Paille also sustained an undisclosed injury in the third period. Julien said he didn't think Paille would make the trip to New York.