Marc-Andre Fleury stopped 18 shots for the Penguins, who have lost two straight on the heels of a four-game winning streak.
"It's tough becasue the guys are out there playing hard," said Fleury. "We're giving it our all every night, but you can't win every game."
Trailing 2-0, Pittsburgh got on the board via the power play. Matt Niskanen missed the net with a point shot, but Chris Kunitz hammered home the carom off the end boards at the left post 35 seconds shy of the midway point of the third period.
New Jersey captain Zach Parise sealed the win with an empty-net tally inside the final minute.
The Devils built that two-goal lead in the first period.
Penguins defenseman Brooks Orpik covered the puck in the crease and Kovalchuk beat Fleury on the subsequent penalty shot to open the scoring at the 14:43 mark.
New Jersey then converted on a 5-on-3 with 24 seconds remaining. Elias hit the far post with a shot from the right wing, but David Clarkson didn't miss from in tight.
New Jersey finished the 2011 calendar year with 49 wins, tops among all Atlantic Division clubs...Pittsburgh's Evgeni Malkin had his point streak snapped at nine games...Coming in, the Penguins had won the three previous meetings.