The Devils' Patrick Elias had forged a 1-1 tie less than 2 minutes into the third with snap shot past Marc-Andre Fleury, but Kunitz quickly responded with the go-ahead tally 3:07 into the frame.
Staal, who also scored in the opening period, then doubled the Penguins' advantage on a backhander at 4:17.
James Neal notched his eighth goal of the year and Fleury turned aside 23-of-24 shots for Atlantic Division leading-Pittsburgh, which won its third straight contest.
Johan Hedberg made 25 saves for New Jersey, which lost for the first time in five games.
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