Evgeni Malkin recorded three shots in his return to the Pittsburgh lineup. He had missed the last five contests and seven of eight with a sore right knee -- the same one that the Russian forward had season-ending surgery on in February.
Evgeni Nabokov made 26 saves for New York, which suffered its third straight loss.
Dupuis scored on a breakaway with 2:54 remaining in the first period, then Park, a former Islander, fired a shot off Nabokov's left shoulder 21 seconds into the middle frame.
Staal hit an empty net to seal the win with 2:00 minutes to play in the third.
Fleury has 20 career shutouts...The Penguins improved to 16-2-2 in their last 20 games against the Islanders...Pittsburgh's Dan Bylsma coached his 200th NHL game on Tuesday...Islanders forward Matt Moulson played in his 200th career game...Park was an Islander for four seasons from 2006-10...Both teams were 0- for-2 on the power play...The Penguins have killed all but one of their opponents' 35 power-play opportunities this season...The clubs will meet Thursday in Pittsburgh.