The Devils stretched their unbeaten streak to 11 games.
Defenseman Brian Rafalski intercepted a pass in his own zone and quickly dished to Elias, who broke out on a one on one. The Devils' leading scorer each of the last four seasons unleashed a wrist shot from the high slot that beat rookie goaltender Marc-Andre Fleury to the left side.
Elias gave New Jersey a 1-0 lead 3:45 into the game and Martin Brodeur made it stand until Penguins defenseman Dick Tarnstrom converted a cross-crease pass from Aleksey Morozov for a power-play tally with 27 seconds left in the third.
Brodeur finished with 18 saves while Fleury, who also was on the short end of a 2-1 decision against the Devils on Oct. 24, turned aside 31.