The drive might have clipped Islanders forward Brad Boyes on its way past goalie Evgeni Nabokov.
The Penguins dominated even with Evgeni Malkin sitting out 17 games due a lingering shoulder problem.
New York already has veteran goalies Evgeni Nabokov and Rick DiPietro on its active roster.
Evgeni Malkin moved the puck from behind the net to Tyler Kennedy, who fed it to Orpik.
But the Penguins answered each goal, and Orpik's shot eluded the right arm of Islanders goaltender Evgeni Nabokov.
Crosby fed Kunitz in the slot for a hard shot that beat goalie Evgeni Nabokov to win it.
The Penguins have talented offensive players, such as Evgeni Malkin, but they are still hard to score on.
Evgeni Malkin added two assists, and Marc-Andre Fleury made 32 saves for Pittsburgh.
Evgeni Nabokov stopped just 12 of 17 shots in two periods before getting pulled for the final 20 minutes.
The 31-year-old DiPietro has played in only three games this season while serving as the backup to Evgeni Nabokov.
Tavares slammed in his own rebound in front after Brad Boyes fed him following a turnover by Penguins star Evgeni Malkin.
Orpik, a defenseman, took a shot from the left point that found its way through traffic and got past goalie Evgeni Nabokov.
Evgeni Nabokov overcame a sloppy start to make 30 saves as the youthful Islanders weathered the comeback of the NHL's best player.
Evgeni Nabokov helped spearhead a late surge that saw the Islanders lost just once in regulation for the season's final three weeks.
Matt Cooke, Jay McKee, Ruslan Fedotenko, Mike Rupp, Brent Johnson, Evgeni Malkin.
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Islanders goaltender Evgeni Nabokov actually has worse statistics in this series than Fleury, with a 4.56 goals-against average and an .846 save percentage.
Evgeni Nabokov overcame a sluggish start to stop 30 shots and the Islanders won their first playoff game in more than six years.
Eleven players on their roster are 25 or younger, yet their goaltender, Evgeni Nabokov, is 37, and their top defenseman, Visnovsky, is 36.
"I'm always telling the guys that it's all about consistency from shift to shift, " said winning goaltender Evgeni Nabokov, who stopped 29 shots.
Kennedy greedily accepted the puck at New York's blue line, then flipped a wrist shot over Evgeni Nabokov's glove to give Pittsburgh the lead.
Evgeni Nabokov didn't leave anything to chance Sunday night, posting a shutout to make sure they headed out on the road on a positive note.
Kane thought Jokinen would bury the shot behind Islanders goalie Evgeni Nabokov, but the puck rolled along the goal line and he poked it over.
Pittsburgh made the most of limited pressure on goalie Evgeni Nabokov.
Evgeni Nabokov, the Islanders' goaltender, was not a whole lot better Tuesday than Pittsburgh goaltender Marc-Andre Fleury, but Nabokov held on to the last Islanders' lead.
The Rangers earned the power play when Michael Del Zotto was hauled down as he crashed in on Islanders goalie Evgeni Nabokov 21 seconds into overtime.
It was the first appearance in a home game for the oft-injured goalie, who has lost his starting job to Evgeni Nabokov, since Nov. 23, 2011.
Doug Murray and Kris Letang also scored for Pittsburgh, who chased New York goaltender Evgeni Nabokov after Letang's goal made it 4-0 early in the third period.
Poulin was making his third start of the season to give a rest to Evgeni Nabokov, who has started all but six of the team's 37 games.
The result was an electric power play goal early in the third period where Crosby took a pass from Evgeni Malkin then fired a laser at Neal's stick.
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