Marek Hamsik handed the hosts an early lead by scoring his first goal of the campaign with a low, angled shot in the fourth minute.
Top-scorer Dries Mertens then netted his ninth goal in all competitions this season by slotting home from the penalty spot five minutes before the interval.
Kalidou Koulibaly rounded off the win with a close-range finish two minutes into the second period.
Second-placed Juventus had started the day on the same number of points as Napoli but lost their perfect Serie A record when they were held to a 2-2 draw away at Atalanta.
Federico Bernardeschi and Gonzalo Higuain put the champions 2-0 up inside 24 minutes, but Mattia Caldara and Bryan Cristante scored either side of the interval to earn the hosts a point.
Massimiliano Allegri's side have been joined on 19 points by Inter Milan, who defeated Benevento 2-1 away thanks to a Marcelo Brozovic double.
Juventus retain second place in the table thanks to a superior goal difference.
Lazio will go into the international break in fourth place, five points adrift of Napoli, after beating Sassuolo 6-1 at the Stadio Olimpico.
Luis Alberto and Marco Parolo both scored braces for Simone Inzaghi's side, while Stefan de Vrij and Ciro Immobile completed the rout.
(Reporting by Matt Westby; Editing by Christian Radnedge)
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