The visitors took the lead late in the first-half when Gianluca Musacci brought down Edinson Cavani in the penalty area. The Uruguayan took the spot-kick himself and, although he was denied by a superb Antonio Mirante save, Cavani calmly netted from the rebound.
With 20 minutes remaining, Napoli keeper Morgan De Sanctis could only parry Gabriel Paletta's well-struck shot and Cristian Zaccardo netted from close range.
The goal gave Parma belief and they looked to be the more likely side to win the game, but in the 86th minute, Cavani received the ball on the edge of the box and slid in to Lavezzi to clinically finish low across the keeper.
The victory keeps fifth-placed Napoli in contention for Champions League place.