The Packers, behind substitute quarterback Scott Tolzien, had pulled to within 20-13 early in the fourth quarter after a long touchdown drive.
But on the next series, he ran out of the pocket and his pass attempt was picked off by Pierre-Paul, who ran untouched into the end zone for the game-clinching score with 10:49 remaining.
Tolzein was intercepted three times in all as the Packers (5-5) dropped their third straight after star signal-caller Aaron Rodgers went down with a broken collarbone.
Eli Manning completed 25-of-35 passes for 279 yards and a touchdown pass to Rueben Randle for New York (4-6), which logged a fourth straight win following an 0-6 start.
Victor Cruz made eight catches for 110 yards.
Jordy Nelson led the Packers' receiving corps with eight grabs for 117 yards.