Kunitz's five-point performance was a career high and Crosby's five assists tied a personal best as the Penguins reeled off a fifth straight win.
Tomas Vokoun turned aside 23-of-24 shots to earn the win.
Starting Islanders goalie Evgeni Nabokov was pulled after two periods. He was torched for five goals on 17 shots.
Kevin Poulin stopped 10-of-11 shots the rest of the way.
Brad Boyes netted New York's only goal.