Parma may have opened the scoring via Raffaele Palladino, but a strong second-half performance by the Azzurri has seen them claim maximum points.
Raffaele Palladino opened the scoring just before the half-hour mark, but two goals within five minutes after the restart shifted momentum the Azzurri's way. The right-back secured maximum points late in the encounter.
The home side started the more optimistic, and Palladino looked to break the deadlock after only two minutes. Capitalising on a Fabiano Santacroce error, the striker pushed forward, fending off the stopper, but fired his right-footed shot across Morgan De Sanctis' goal.
Napoli's first foray forward almost resulted in a goal, as Maggio's cross fell kindly into the path of Edinson Cavani, but his driving shot was deflected away off Francesco Valiani.
Palladino took full advantage of another defensive error, and this time, made the Azzurri pay. The visitors failed to clear their defensive lines properly from a corner kick on 29 minutes, and with the ball falling into the striker's path, he sweetly timed his volley and found the top-right corner to make it 1-0.
The goal sprung the visitors to life, and they began to raise the rhythm of the match. Juan Zuniga managed to deliver a ball into the middle, and Maggio couldn't quite direct his header on target on 35 minutes.
Marek Hamsik brought the Partenopei back into the match six minutes after the restart. Ezequiel Lavezzi did the hard work to weave past Daniele Galloppa and stride into the box, squaring a pass for the Slovakian international, who tapped the ball past Antonio Mirante to make it 1-1.
The Ducali defence was sliced apart once again on 57 minutes, as Hamsik threaded a perfect pass for Lavezzi to run onto and slot home to give the visitors a 2-1 lead.
The match went from bad to worse for Parma as Daniele Galloppa was given his marching orders for a high boot on Hamsik just before the hour mark.
With the lead and numerical advantage, Napoli looked to go on the assault.
Sebastian Giovinco almost equalised on 72 minutes as he swung in a dangerous free-kick from the left. De Sanctis could only get a fingertip to the ball, but it was scrappily cleared.
Zuniga and Cavani broke away for a two-on-one counterattacking opportunity, with only Paci to beat, but an overhit pass by the left-back saw the move fizzle away.
Maggio secured all three points with three minutes to go as the right-back got into a good position and punished Paci's poor attempts at clearing his line to make it 3-1.
The win lifts Napoli back into third position after being overtaken by Udinese earlier in the day, whilst leaving Parma only a point above the relegation zone.