Ezequiel Lavezzi, Hugo Campagnaro and Marek Hamsik were all on target for the visitors with Roberto Guana scoring for the home side, who ended the game with 10 men following the dismissal of Yohan Benalouane early in the second half.
The result will send Napoli into their midweek Champions League clash at Manchester City full of confidence.
Benalouane almost gave the home side a dream start in the second minute when he glanced a header just wide of an unguarded far post from a corner.
Lavezzi put Napoli in front less than a minute later, though, as the Cesena defence suffered a mental lapse.
Hugo Campagnaro was able to send a throw-in from the halfway line to Lavezzi, who had been left all alone inside the Cesena penalty area, and he beat the home team's debutant goalkeeper Nicola Ravaglia with a shot inside his near post.
Cesena were doing most of the attacking, but the best chances still fell at the other end.
A 21st-minute cross from Andrea Dossena was met on the volley by Christian Maggio, but he sent the ball wide, and in the 36th minute a good team move saw Mario Santana square the ball to Lavezzi, who flashed his shot wide of the post.
In between those chances, Guana brought Cesena level as he lunged in to meet Eder's cross ahead of Paolo Cannavaro and diverted the ball into the far corner of Morgan De Sanctis' goal.
Napoli looked brighter earlier in the second half and their cause was helped by a red card for Benalouane, who handled Campagnaro's through-ball towards Edinson Cavani to earn a second yellow card in the 55th minute.
Cannavaro had a header cleared off the line by Antonio Candreva 10 minutes later, but from the resulting corner the visitors went in front again.
The ball was pulled back to Blerim Dzemaili, whose low cross was met at the far post by Campagnaro, who slid in to lift the ball into the roof of the net from close range.
Napoli substitute Goran Pandev then delivered an early contender for miss of the season when he managed to shoot against the crossbar from just seven yards out with an open goal to aim at in the 85th minute.
It did not matter too much, though, as Hamsik made it three shortly afterwards with a powerful shot from just inside the penalty area allowing Napoli to relax a little more for the final few minutes.