Jaroslav Halak had 26 saves against his former team while losing for the third time in three starts for the Rangers, who have lost four straight (0-2-2) after a 3-1-0 start.
After a scoreless first, Palmieri broke through at 8:44 of the second, rifling the puck past Halak for his first of the season.
Bailey made it 2-0 at 5:37 of the third with his first and Palmieri capped the scoring with 4:38 remaining.
Sorokin made 17 saves in the first, 12 in the second and 12 more in the third for his 11th career shutout. He had seven shutouts last season.
The long-time rivals split four games last season — with the road team winning each time. However, the Islanders have now won seven of the last nine meetings and are 9-4-0 against the Rangers since January 2021.
The Islanders were 0 for 2 on the power play, while the Rangers failed on their lone opportunity.
Halak played four seasons for the Islanders including a 38-win campaign in 2014-15. After leaving Long Island, he spent three seasons with Boston and one in Vancouver before signing with the Rangers in the offseason to back up reigning Vezina Trophy-winner Igor Shesterkin.
Before the game, hockey historian and former Islanders broadcaster Stan Fischler was honored by having the press level at UBS Arena dedicated and named for him. The 90-year-old “Hockey Maven” has been working in hockey since 1954 when started with the Rangers in their press office. He has written more than 100 books on the sport, was a television commentator on Islanders telecasts for more than four decades and helped start the careers of dozens of future hockey journalists who worked for him as interns. He is still writing for The Hockey News.
Islanders forward Josh Bailey played his 999th NHL game.
Rangers: At Dallas on Saturday.
Islanders: At Carolina on Friday night.
Allan Kreda, The Associated Press