The Italy international netted a vital goal to keep Roberto Donadoni's men in the race for Europa League qualification.
The guests had a goal disallowed for offside in the opening 45 minutes before Marco Parolo netted the only goal of the game in the second half.
The away side thought it had taken the lead after 10 minutes of play when Federico Fernandez found the net after a Lorenzo Insigne free kick, but the referee disallowed the goal for offside.
Another Insigne set piece saw Jose Callejon pop up in a dangerous situation, yet the Spaniard had to settle for a corner as his attempt at the far post deflected wide.
Parma then threatened halfway through the first half when Jonathan Biabiany attempted to set up Rafael Palladino, only for Raul Albiol to frustrate the hosts with a fine interception.
The home side again looked dangerous in the closing minutes of the first period after Afriyie Acquah found Gabriel Paletta, yet the Italy international's header went over the crossbar.
Pepe Reina was called into action shortly after the break as Biabiany sent in a dangerous low shot, and the goalkeeper did well to divert the danger.
There was little Reina could do about Parma's 55th minute opener, however. Mattia Cassani found Parolo at the edge of the area with a pinpoint cross and the midfielder coolly slotted home to make it 1-0.
Gonzalo Higuain came close to leveling the scoring after a superb pass from Jorginho, yet the former Real Madrid man fired wide from a difficult position.
Duvan Zapata felt he should have been awarded a spot kick in the 76th minute after he went down following Antonio Mirante's touch, only for the referee to book the Colombian forward for diving.
Insigne got a big chance to restore parity after 83 minutes of play following a fine cross from Dries Mertens, but the winger failed to hit the target, while Zupata headed inches over from close range only minutes later.
Parma has climbed to joint fifth spot in the Serie A table following this weekend's results, while Napoli remains third in the standings.