Rafael Benitez’s side remain four points behind second-placed Roma, who fell weakly 2-0 at AC Milan on Saturday night, and three behind Lazio, who were beaten 2-1 by Inter Milan??on Sunday.
Raffaele Palladino fired Parma ahead, with Cristobal Jorquera restoring their lead after Manolo Gabbiadini plundered an equaliser.
Dries Mertens would force the draw in the second half but Napoli are running out of time to gatecrash the top three with only three games remaining.
Hernanes scored twice against his former club Lazio to launch Inter up the table with a 2-1 win.
Antonio Candreva got Lazio off to a good start but the Brazilian playmaker who once dazzled at the Stadio Olimpico went on to twice exploit lapses in discipline from Champions League-chasing Lazio.
He converted a free-kick after Mauricio was sent off and made use of the extra space created when goalkeeper Federico Marchetti saw red – Mauro Icardi had missed from the spot but Hernanes made amends late on.
Fiorentina edged a topsy-turvy Tuscan derby meeting with Empoli to remain in the frame for a fourth-placed finish.
Two goals from Josip Ilicic proved key in a 3-2 victory at the Stadio Carlo Castellani that moved La Viola to within five points of Napoli.
Riccardo Saponara and substitute Levan Mchedlidze scored for 13th-placed Empoli, while Mohamed Salah’s odd goal in five arrived shortly after half-time and gave Fiorentina the momentum they needed to ride out the win.
Sampdoria are six points behind Napoli in sixth place after hammering Udinese 4-1 with a brace from Roberto Soriano and two more from Afriyie Acquah and Alfred Duncan.??
Antonio Di Natale netted a consolation effort from the penalty spot for Udinese.
Cesena’s relegation was confirmed as they let a two-goal lead slip to lose 3-2 at home to Sassuolo.
Goals from Simone Zaza, Saphir Taider and Simone Missiroli cancelled out earlier strikes from Gregoire Defrel and Franco Brienza.
Ten-man Atalanta??boosted their survival hopes with a 3-2 triumph at Palermo.
Daniele Baselli set the visitors on their way before an own goal from Sinisa Adelkovic doubled Atalanta’s advantage. Palermo’s Franco Vazquez reduced the deficit but Alejandro Gomez extended Atalanta’s lead.
Atalanta then lost goalkeeper Vlada Avramov to a red card after he brought down Vazquez in the area.
Andrea Belotti struck the resulting spot-kick past substitute goalkeeper Giorgio Frezzolini but his powerful attempt hit the crossbar.
Luca Rigoni made it 3-2 but the Bergamaschi held on for a vital win, likely enough to see them safe.
Chievo and Hellas Verona drew 2-2 in their city derby with every goal arriving in a thrilling first half.
Alberto Paloschi put Chievo ahead but Hellas hit back with goals from Juanito and Luca Toni. The Flying Donkeys equalised from the penalty spot after Sergio Pellissier earned and converted a penalty.