New York, which had won two consecutive games, seized an early 2-0 lead before being steamrolled by the Pittsburgh surge.
A power-play goal from Kris Letang put the Penguins ahead by two and although the Islanders twice moved within one they could not rally all the way back.
Brandon Sutter's empty-net goal with four seconds to play clinched the victory, Pittsburgh's second in a row. The Penguins boosted their lead over the New York Rangers in the Metropolitan Division to 17 points.
The win went to Jeff Zatkoff, who made 30 saves. Kevin Poulin gave up five goals on 28 shots.