Ezequiel Lavezzi celebrates scoring the winner after Marek Hamsik had dragged Napoli level against Parma.
Napoli got back to winning ways as the race for the Scudetto warmed up as they beat Parma 3-1 on Sunday.
League leaders AC Milan, still smarting from their European Champions League loss to Tottenham Hotspur, suffered a surprise 1- 1 draw with lowly Bari, leaving the title race still open for Inter and Napoli.
Raffaele Palladino gave Parma a deserved lead in the 29th minute, but Napoli recovered in the second half with Marek Hamsik securing the equalizer and Ezequiel Lavezzi putting Napoli ahead in the 56th minute.
Daniele Galloppa was given his marching orders for a dangerous foul on Hamsik in the 59th minute and Christian Maggio sealed the win for Napoli three minutes from time. As a result, Napoli narrow the gap on league leaders AC Milan to six points, moving back above Udinese into third place, just one point adrift of second-place Inter Milan.
Earlier, ten-man AC Milan rallied for a draw with last-place Bari after Zlatan Ibrahimovic was sent off for punching an opponent in the stomach.
Second-half substitute Antonio Cassano scored in the 82nd minute for the Serie A leaders following a superb cross from Luca Antonini at the San Siro.
Hungary forward Gergely Rudolf had put Bari ahead in the 39th, finishing off a perfectly executed set piece.
Ibrahimovic was given a straight red card for hitting Marco Rossi in the 73rd after the defender beat him to a header.
Milan restored its five-point lead over Inter Milan after their city rivals were held to a 1-1 draw at Brescia on Friday.
Elsewhere, Antonio Di Natale raised his league-best scoring total to 24 goals as Udinese won 4-0 at Cagliari to join Napoli in third place, nine points behind Milan.
Roma captain Francesco Totti scored twice in a 2-0 derby win over Lazio, Roma's fifth consecutive win over their city rivals.
Roma midfielder David Pizarro hit the crossbar five minutes in at the Stadio Olimpico. Lazio's Cristian Ledesma and Sergio Floccari both missed decent chances before Lazio goalkeeper Fernando Muslera was unable to handle Totti's free kick as Lazio's wall fell apart in the 70th.
Totti then added a penalty in added time, taking him to 199 goals in a glittering Serie A career and securing a victory that lifts Roma's spirits after their elimination from the Champions League by Shakhtar Donetsk last week.
Lazio defender Stefan Radu was sent off for headbutting Roma midfielder Fabio Simplicio in the 88th. Simplicio was then brought down inside the area in the 90th to set up Totti's penalty. Ledesma was sent off for his protests, leaving Lazio with nine men.
In other matches on a rainy day up and down the peninsula, Catania beat Sampdoria 1-0, Chievo lost to Fiorentina 1-0, Genoa beat Palermo 1-0, and Lecce lost to Bologna 1-0.
