Brock Nelson scored his second of the game into an empty net with 25 seconds left for the 4-2 final.
"Hockey's a game of momentum," Pittsburgh coach Mike Sullivan said. "I thought we pushed back. We had a lot of quality looks. … Instead of finding a way to win, we found a way to lose."
Ilya Sorokin made 44 saves for the Islanders (29-24-7), who also came back from down one in the third to defeat the Penguins 5-4 at home on Friday.
New York was playing its first game without forward Mathew Barzal, who is out week to week with a lower-body injury.
"We needed our goalie to be good. He was," Islanders coach Lane Lambert said. "We have a great rivalry with this team. The way the game ended the other night in New York, I expected this to be a hard-fought game. We're both fighting for points."
Jake Guentzel and Jason Zucker scored for the Penguins (27-20-9), who have lost three in a row. Jarry made 28 saves in his return after missing nine games with an upper-body injury.
"It's obviously tough this time of year to come back in," Jarry said. "You don't have many practices, you don't have many opportunities to skate, so I think that's the toughest thing is just getting back into game action. It's always tough when you've almost had two months off."