Pittsburgh goaltender Marc-Andre Fleury made two important saves in the final 30 seconds to seal the win, after the Hurricanes mounted a spirited fightback late in the game.
Philippe Boucher converted a power-play at 11:33 in the third to give the Penguins a comfortable 3-1 lead after early goals to team mates Miroslav Satan and Evgeni Malkin.
But the Hurricanes hit back with an empty-net goal from Joe Corvo with 1:26 left, sparking a late flurry of forward thrusts as Carolina frantically searched for an equaliser.
With 28 seconds remaining, Eric Staal found himself in front of an open net, but could not control the puck. A weak wrister from the Carolina center was duly corralled by a relieved Fleury.
"I was in trouble. It's a good thing for me he didn't get good wood on it," Fleury told reporters.
Chad LaRose scored Carolina's opening goal.
The hapless Hurricanes, taken to game seven in both their quarter and semi-final series, may also face the prospect of a depleted lineup going into game two in Pittsburgh on Thursday, after injuries to wingers Erik Cole and Tuomo Ruutu.
Cole came off worse in a bone-jarring knee-to-knee collision with Penguins winger Matt Cooke in the third period, while Ruutu was clipped from behind in the first.
