The leaders were thumped 4-0 at home by Milan last weekend, but they bounced back by overcoming a stubborn Lecce, who can count themselves unlucky not to come away with a share of the spoils on Friday.
Giovanni Di Lorenzo headed Napoli in front early on, but the hosts equalised not long after halftime when Federico Di Francesco thumped home with a fine finish.
An own goal later gave Luciano Spalletti's men victory as Mario Rui's teasing delivery came off Antonino Gallo, with Falcone only able to paw it over the line as Napoli resumed normal service.
The hosts had started brightly, Youssef Maleh forcing a great save from Alex Meret to palm over his rasping drive.
The visitors grew into the game though, and Di Lorenzo put them ahead in the 18th minute when he sent a powerful header from Kim Min-jae's cross flying past Falcone.
A fingertip save from Falcone pushed Hirving Lozano's low shot past the post to keep Napoli's lead at just a single goal heading into the break, and Lecce levelled shortly after the interval.
A free-kick into the visitors' box caused havoc, and Assan Ceesay saw a header come back off the bar before Di Francesco rifled into the bottom corner.
Napoli went on to win in bizarre fashion, though, as a mix-up between Gallo and Falcone from Mario Rui's cross ended with the goalkeeper clawing into his own net to give the league leaders their 24th Serie A win of the campaign.
With nine games left to play, Napoli's win was another step closer to ending their 33-year wait to win the Serie A title.
Second-placed Lazio will be in action against Juventus on Saturday.
AAP
