Rafael Benitez's side were made to work hard for the points against a resilient Nerazzurri side, whose hopes of holding out evaporated once Luca Cigarini was sent off soon after Gonzalo Higuain had sent the home fans into delirium.
Jose Callejon then wrapped up victory late on to extend Napoli's 100 per cent winning start to the season.
Mario Balotelli spared AC Milan from serious embarrassment with the last kick of a dramatic 2-2 draw at Torino, who were denied their first win over the Rossoneri in 12 years.
The focus was supposed to be on Kaka, who was making his long-awaited second debut for Milan after spending four years at Real Madrid, but Torino stole his thunder with a double salvo in the second half.
Captain Danilo D'Ambrosio and Alessio Cerci set Il Toro on course for a first win over Milan since November 2001 and Sulley Muntari's sloppy response seemed to have arrived much too late.
Balotelli had cut an anonymous figure through 90 minutes in Turin but stole the headlines by converting a penalty - won by Andrea Poli - four minutes into stoppage time.
Inter Milan and Juventus shared the spoils from the first Derby d'Italia of the new season as Arturo Vidal salvaged a 1-1 draw for the reigning champions.
The home side broke the deadlock midway through the second half at San Siro as substitute Mauro Icardi scored his first goal in Nerazzurri colours, but Chilean midfielder Vidal responded with his 20th league goal for the Turin giants.
Saturday's Serie A Results