A high sticking call to David Clarkson 5:31 into the first led to a Pittsburgh power play and Staal got the goal as he one-timed a short pass from Park at the left circle into the right corner of the net.
The score stayed that way until the third period when Petr Sykora was issued a double minor for high sticking.
It was Elias' stick that hit the Penguin in the face, but Sykora was sent to the box and the Devils were able to take advantage of the miscue from the referees.
Skating into the Pittsburgh end down the left side, Ilya Kovalchuk sent a backhand pass from the left circle on the fly that was slowed down by a defender, but got through and Elias one-timed it home at the 1:47 mark to tie the game.
However, the game was tied for just 80 seconds as Pittsburgh scored on the second minor when a pass from the high slot by Kris Letang went over to the right circle where Kunitz one-timed it home.
Just 1:10 later, Staal notched his second goal of the game when he got the puck in the slot, cut over to the right side to get past Kovalchuk and lifted a backhander into the net for a 3-1 lead.
Five minutes later it was a 4-1 game when Neal dug the puck out of a scrum along the right boards and turned around before throwing a quick shot on net that fooled Hedberg.
Pittsburgh center Evgeni Malkin sat out a fifth straight game with soreness in his surgically repaired right knee...Pittsburgh starts a home-and-home set with the Islanders in New York on Tuesday...New Jersey continues its four-game road trip in Los Angeles on Tuesday...Pittsburgh took four of six from New Jersey last season.