Without their coach Rafael Benitez, who was sitting out a one-game ban, the Azzurri fell behind to a Gregoire Defrel goal after 15 minutes on Monday night.
Dries Mertens and Manolo Gabbiadini replied with two goals in as many minutes turning the game around, but Defrel struck again just before half-time.
Another Mertens strike in the 57th minute was enough to earn Napoli a crucial win, taking them back to within three points of third-placed Lazio, the side they face at home on the final day of the season in what could be a decider for a place in the Champions League next season.
Napoli had some making up to do to their fans after seeing their dreams of winning the Europa League shattered by Dnipro on Thursday and the last thing they needed was to fall behind early on.
That is what happened, though, with a disorganised defence standing back and allowing Defrel to fire Cesena in front from 25 yards.
Napoli’s season has consisted of ups, downs and inconsistencies and it has been precisely in the moments of difficulty when they have risen to the occasion, and that happened in the 19th and 20th minutes.
Mertens first brought them level with a determined shot from close range after Jose Callejon’s shot took a deflection to fall kindly for the Belgian.
He then turned provider for Gabbiadini by beating two defenders to cross for the former Sampdoria forward to net his 15th goal of the season from five yards out.
Napoli again took the foot off the accelerator when they appeared to be cruising, and they were punished on the stroke of half-time when Defrel punished some more weak neglectful defending by lashing in from close to the penalty spot.
The hosts rolled their sleeves up once again and, after Mertens missed the target when he would have been better off trying to set up Gabbiadini, he added to his earlier goal to put Napoli in front for the second time in the 57th minute.
This time it was enough to earn all three points, although there were still a few scares along the way.
Mariano Andujar did well to turn a Franco Brienza effort behind while Emmanuel Cascione sent an acrobatic effort over the crossbar as Cesena went down fighting.