Hudson Fasching and Brock Nelson each had two assists and Ilya Sorokin made with 19 saves in his 100th NHL appearance. New York has won two in a row.
''Top to bottom it was a great game,'' Barzal said. ''It's a great hockey team over there, it's nice to know we can compete with the best.''
Pierre-Olivier Joseph scored for Pittsburgh and Tristan Jarry made 38 saves, but the Penguins fell for the third time in four games after starting December with a seven-game winning streak.
The Islanders extended their lead to 4-1 with three goals in the middle frame.
Barzal scored his sixth of the season and gave the Islanders a 2-1 lead in the opening minute of the second period. The 25-year-old center skillfully redirected Fasching's shot from the slot past Jarry.
''Might have been the worst game of the year,'' Penguins coach Mike Sullivan said.
Bailey buried a pretty feed from Noah Dobson midway through the second.
Barzal capped the Islanders' three-goal second period with 3:18 left. Fasching won a few battles behind the Penguins goalie and the puck trickled to Barzal's stick before No. 13 fired a wrist shot into the top corner.
New York outshot Pittsburgh 20-4 in the second period
''The forwards did a good job staying above them, taking away their time and space,'' Dobson said about his teammates. ''They weren't able to get on their forecheck and we were able to keep good gaps. We have to be moving pucks quick, when we play fast, we are tough to handle.''
Lee opened the scoring with his 12th of the season 1:03 into the first period. Penguins alternate captain Evegni Malkin fumbled the puck inside the defensive zone and Nelson set up the Islanders captain. New York improved to 13-4-0 when scoring the first goal this season.
Joseph evened it at 1 with 4:47 left in the first period when he fired a shot from the point past Sorokin.
''They are a tight-checking team, you have to work for everything,'' Jeff Carter said. ''The compete level could have been a lot higher from everybody.''
Lee picked up his second goal of the game when he deposited a rebound at 3:33 of the third period to stretch the Islanders lead to four goals.
''You can't really give these guys much time or space,'' Lee said. ''You don't want to keep them around, that's a talented team that's been rolling pretty good. We have seen them a lot and know their ability to close in on a game pretty quickly.''
Islanders forward Oliver Wahlstrom left the game after sustaining an upper-body injury on his first shift of the game and did not return. Wahlstrom delivered a huge check on Penguins defenseman Chad Ruhwedel early in the first period. Joseph, Ruhwedel's defensive partner, drove Wahlstrom's head into the boards in an effort to stand up for his teammate.
Zach Parise played in his 118th consecutive Islanders game and has played in every game since joining the team in October 2021 after the Minnesota Wild bought out the final four years of his contract in the summer of 2021. It is the 24th-longest active streak in the NHL.
Islanders: Host Columbus on Thursday night.
Penguins: Host Detroit on Wednesday night.
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