Napoli remain in third spot on 38 points, one point off leaders Inter Milan, who are away to Parma later on Wednesday. Verona stay third from bottom, the final relegation spot, on 13 points, two points off 17th-placed Genoa.
Napoli came into the match on the back of four consecutive wins, including their Super Cup success, without conceding while Verona had lost their last two, both by a 3-0 scoreline but the visitors came close to pulling off a famous win.
The hosts were on the attack early and the first chance fell to Eljif Elmas, whose shot was saved by Verona keeper Lorenzo Montipo.
Despite dominating possession, that would prove to be Napoli’s only effort on target in the opening half while Verona made the most of their quick counter-attacking play.
Gift Orban tried his luck from distance, his deflected shot easily gathered by Napoli keeper Vanja Milinkovic-Savic before the visitors took a shock lead in the 16th minute.
Cheikh Niasse played a low pass into the six-yard area and the unmarked Martin Frese scored with a delightful backheel.
Things got even worse for the hosts when Verona were awarded a penalty for an Alessandro Buongiorno handball.
Orban stepped up with boos ringing out around the Stadio Diego Armando Maradona but he kept his cool and buried the spot kick into the bottom corner in the 27th minute.
Rasmus Hojlund headed over a Giovanni Di Lorenzo cross as Napoli struggled to find a way back into the game and Verona held firm to take their lead into the break.
Napoli piled forward after the interval, and pulled one back from a corner in the 54th minute.
Scott McTominay sent a glancing header goalwards and defender Nicolas Valentini’s desperate attempt to head clear ended up in his own net.
Verona found their feet again and Antoine Bernede sent a scorching shot over from the edge of the area.
Napoli thought they had levelled 18 minutes from time but a VAR check chalked off Hojlund’s effort for handball, and minutes later an offside call denied Amir Rrahmani an equaliser but the goal came eight minutes from the end.
Luca Marianucci played a pass into the area which Di Lorenzo met first time to steer his shot past Montipo.
Verona, whose last win away to Napoli came in 1983, hung on under extreme pressure but came close to snatching an added-time winner with Giovane’s attempted chip going narrowly wide.