Edinson Cavani scored his league-leading 18th goal in Serie A this season to take Napoli to within three points of leaders Juventus as Parma lost their unbeaten home record on Sunday.
Juventus had spurned the chance to secure an eight-point lead on Saturday when they were denied a last-gasp penalty in a 1-1 draw at home to Genoa.
It gave Napoli an extra incentive on Sunday, but Walter Mazzarri's side were made to work by a Parma side battling to protect their impressive unbeaten record at home.
Napoli opened the scoring in the 20th minute through Marek Hamsik only for defender Paolo Cannavaro to turn Nicola Sansone's shot across goal into his own net for Parma's second-half equaliser.
In the 85th minute, however, Cavani ran on to a through ball and rounded Mirante to seal the win with a classy finish.
Napoli remain second on 46 points but are now just three behind Juve and three clear of Lazio, who were stunned 1-0 by Chievo at the Olympic Stadium.
Cannavaro, the brother of former Italy defender Fabio, added: "The title race is neither open nor closed. The important thing is to simply be in the race."
AC Milan survived some tense moments away to Atalanta but emerged with a precious 1-0 win thanks to Stephan El Shaarawy's first-half strike following an M'Baye Niang's through ball.
Milan's 11th win moved them up to fifth, 12 points behind Juve with Fiorentina going the other way after a 2-1 defeat at Catania.
Inter Milan, meanwhile, were left nine points behind Juve after being held 2-2 at the San Siro by a spirited Torino, who notched their 10th draw of the campaign.
Inter got off to the perfect start when Romanian Cristian Chivu sent a sumptuous freekick past Jean-Francois Gillet in the Torino net after five minutes.
But a spectacular mix-up on 23 minutes allowed Toro to pull level.