The Penguins were trailing 3-2 with less than 6 minutes left in the regulation when Paul Martin's shot from the point deflected off New York's Frans Nielsen and got past goalie Evgeni Nabokov for an equalizer.
Then in the overtime, the Pens got control of the puck in the Islanders' zone and Tyler Kennedy sent a pass to the left point, where Orpik unleashed his game-winning scoring blast.
With the victory, Pittsburgh won its Eastern Conference quarterfinal series 4-2 and goes on to play the Ottawa Senators in Round 2. It marked their first post-season series victory in three years.
Tomas Vokoun turned aside 35-of-38 shots for the Penguins.
Nabokov finished with 17 stops.