The hosts took the lead with just nine minutes on the clock when Raffaele Palladino tapped in from close range, before Manolo Gabbiadini got the away side level on 28 minutes after being picked out by Marek Hamsik.
Napoli pushed hard for an equaliser after the break, but Hamsik and Jose Callejon were both denied by Antonio Mirante. Mirante came to Parma's rescue again soon after, keeping out efforts from Gonzalo Higuain and Gabbiadini as Napoli grew increasingly frustrated.
Despite their failure to convert a handful of chances, the visitors finally got an equaliser with just under 20 minutes to play when Dries Mertens found the bottom corner after being fed by Ivan Strinic.
Both teams tried to force a winner during the final stages, but Silvestre Varela was thwarted by Andujar before Hamsik and Higuain were again kept out by Mirante at the other end.