The Penguins, No. 1 seed in the Eastern Conference, made a statement in the opening game of their Eastern Conference quarterfinal series.
Pittsburgh's one-sided victory came without superstar Sidney Crosby, who has not yet been cleared for action after suffering a broken jaw on March 30. The Penguins will host Game 2 on Friday.
The shutout was the sixth for Fleury in 76 career playoff appearances. He made 26 saves as he seeks to repeat his 2009 performance in which he was the winning goaltender in all of Pittsburgh's 16 victories en route to the Stanley Cup.
Beau Bennett opened the scoring 3:30 into the game and Dupuis produced his first goal with 6:37 left in the opening period.
Kris Letang and Dupuis tallied in a span of 32 seconds early in the second period to break things open and Tanner Glass provided the final Pittsburgh score.
Evgeni Nabokov started in goal for the Islanders, but the two quick goals in the second period drove him from the contest. He allowed four goals on 15 shots before being replaced by Kevin Poulin.