Kyle Okposo scored in the third round of the shootout, sending New York to a 5-4 victory at Pittsburgh.
"That's the sign of a good team, when you don't play well, and you don't stay focused, and you don't do the intangibles that it takes and you still win the hockey game," Islanders coach Jack Capuano said.
Sidney Crosby and New York's Frans Nielsen scored in the second round, and Islanders goaltender Chad Johnson stopped Brandon Sutter. Okposo deked to his forehand, slipping a shot that hit off Marc-Andre Fleury's pad and into the net for the win.
"He came down, I tried to show him something, and it didn't work," said Fleury, who was seeking his 300th career win.
Matt Martin, Nikolay Kulemin and Ryan Strome scored in an impressive flurry in the first, helping New York to the early lead. Strome also had two assists for the Islanders, who have won seven of eight and now trail Pittsburgh by two points in the Metropolitan Division.
"This has been one of our biggest rivals over the last few years, so you always get up for these games," Martin said. "They're the team we're chasing in the standings right now."
Patric Hornqvist forced overtime with his 10th goal of the year for the Penguins, who had won three in a row. Sutter, Blake Comeau and Nick Spaling also scored in regulation.
Kris Letang nearly ended it in overtime for Pittsburgh, but Johnny Boychuk stopped the wraparound attempt when he got his stick on the puck before it crossed the goal line.
New York carried a 4-3 lead into the third period, but Hornqvist tied it with seven minutes left, finishing a one-timer from Evgeni Malkin.
"We were able to get ourselves back in the game," Crosby said. "We just didn't play a full 60 minutes and didn't really deserve to win."
Casey Cizikas nearly put the Islanders ahead, but his one-time redirect hit the post to the right of Fleury.
The teams in the Metropolitan meet again on Saturday in New York.
"We're going to have to play better tomorrow night if we're going to have a chance to win the game," Capuano said. "They're a pretty good hockey club."
The re-tooled Islanders entered with their best start since the 1987-88 season.
The Penguins handed the Islanders their first loss of the season last month during the initial meeting between the teams in Pittsburgh. In that game, New York, which won its first four games of the season, held an early lead before Pittsburgh rallied for a two-goal victory.
The Penguins put together a couple of comebacks on Friday, but Okposo had the winning play for the Islanders.
"The first period, we really didn't give ourselves a chance, the way we played," Crosby said. "They carried the play and got rewarded for it."
The Penguins played their first game without veteran winger Pascal Dupuis, who will miss the rest of the season after blood clots were found in his lungs.
Sutter opened the scoring just 1:13 into the game, but the Islanders controlled the next two periods as Pittsburgh appeared sluggish without its emotional leader, twice falling behind by two goals.
"You don't want to start games like that, especially when important points are on the line," Crosby said.
The Islanders, who allowed the first goal for the fourth straight game, scored three times in 1:35, taking command midway through the first.
Martin started the surge, beating Fleury with a short-side wrist shot during a rush down the left wing.
Kulemin followed 29 seconds later, forcing a Paul Martin turnover at the blue line before working past Letang and beating Fleury with a wrist shot from the slot.
Thomas Hickey's shot from the point deflected off Strome's skate, making it 3-1.
Pittsburgh pulled within one when Comeau, while circling around the net, threw a centering pass in front that hit Matt Martin's skate and trickled across the goal line.
Nick Leddy briefly reclaimed the Islanders' two-goal lead at 5:42 of the second with a one-timer from the faceoff dot, but Spaling got it back for Pittsburgh when he tapped a rebound behind Johnson.
NOTES: Penguins F Craig Adams is within one of 900 career NHL games. ... The Penguins and Islanders will meet three more times this season. ... Pittsburgh scratched Simon Despres, while Brian Strait, Matt Donovan and Cory Conacher were scratches for the Islanders.