Hedberg made 23 saves, one on a third-period penalty shot by Michael Grabner, as the Devils beat the Islanders 1-0, handing New York its 14th loss in 16 games.
Petr Sykora's power-play goal late in the second period gave Hedberg all the support he needed as the Devils handed the Islanders their sixth shutout loss in 20 games this season. Five of those have come at the Nassau Coliseum, where the Islanders were not held scoreless all of last season.
Hedberg preserved the lead with 7:10 remaining in regulation when he denied Grabner on a penalty shot. Grabner was tripped by Ilya Kovalchuk on a breakaway after a giveaway by Adam Larsson, but Hedberg read Grabner's move and easily stopped his backhander.
Hedberg also made a pair of good stops in the final minute as the Islanders pressed for the tie.
"He was great. That's exactly what we need. He's a consummate pro," Devils coach Peter DeBoer said of the 37-year-old, whose shutout was his second of the season and 19th of his NHL career. "He sits and waits his turn, then comes and pitches a game like that."
Hedberg also stopped Grabner on a breakaway earlier in the period -- also set up by a giveaway by Larsson, who was benched after the penalty shot.
Al Montoya, returning from a lower-body injury, stopped 22 shots for the Islanders. New York has just 38 goals through 20 games, the fewest in the NHL, and has been blanked three times while losing its last four games. The Islanders have won just twice in 16 games after a 3-1-0 start.
"We have to score on our chances," Isles center John Tavares said. "We played hard, but that doesn't change the results. Their goalie played well, but we have to find a way to put a few in the net."
The teams finish the home-and-home series Saturday afternoon at the Prudential Center in Newark -- and DeBoer said that despite Hedberg's heroics, he's sticking to his plan to play Brodeur.
The Devils, the NHL's leading penalty-killing team entering the game, gave the PK unit plenty of work in the first period by giving the Islanders three power plays -- and killed them all. In fact, Montoya had the toughest save during the power plays -- he stopped Zach Parise on a shorthanded breakaway and again on the rebound.
"I think they had more chances on the PK than we had on the power play," Isles coach Jack Capuano said. "We had some chances, but didn't do a good job of getting pucks and bodies to the net. We played too much on the perimeter."
New Jersey has killed off 22 consecutive opposition power plays and 51 of the last 52.
"It’s not like we’re looking to try to take penalties," Hedberg said. "But when we’re in that situation, we know we can be successful."
New Jersey took advantage of its first power play to score its only goal at 14:13 of the middle period. With Grabner in the box for hooking Andy Greene, Sykora, stationed in the slot, stopped Larsson's straightaway slapper -- the rookie defenseman's stick shattered on the shot -- and snapped a 20-footer past Montoya.
"We didn’t start the way we wanted to with the penalties and kind of kept ourselves out the game early," DeBoer said, "but our penalty kill and our goaltender bailed us out and gave us a chance to get our legs."