The Riviera side were down to nine men after 79 minutes when Alassane Pléa was sent off for a second yellow card.
The Riviera side were down to nine men after 79 minutes when Alassane Pléa was sent off for a second yellow card just after Vincent Koziello's straight dismissal.
Belgian midfielder Dries Mertens had slotted in the opener after 13 minutes with Jorginho doubling the hosts' account with a penalty after 70 minutes.
It was a third straight defeat for Lucien Favre's side who have lost their first two French Ligue 1 matches, and travelled without Mario Balotelli and new signing Wesley Sneijder.
Napoli, third in Serie A and in the Champions League last 16 last year, were a class above the French punishing defensive errors in front of a delighted 50,000 home fans at the San Paolo Stadium.
"At this stage of the season, we can say we played a great match," said Napoli coach Maurizio Sarri.
"We were playing against a team who were more advanced than us in physical preparations, so the risk was very high."
Napoli took control of the game early with Mertens outwitting the Nice defence and taking advantage of an error by Yoan Cardinale to slot past the advancing Nice goalkeeper.
And in the 70th minute it was again Mertens, brought down by Christophe Jallet, who earned the penalty which Jorginho slotted in.
Despite his initial error Cardinale made some key saves against Joe Callejon (15), Mertens (21) and two Lorenzo Insigne efforts after 42 and 67 minutes.
The Italians also other missed chances to increase their advantage with Insigne hitting the woodwork after 51 minutes.
Nice played the final ten minutes with nine men after first Koziello was shown a straight red card for a dangerous tackle on Piotr Zielinski.
Plea was then dismissed for a second yellow card, allowing the Italians to wrap up a deserved victory ahead of their Serie A opener on Saturday.
Maurizio Sarri's side are now ideally placed to join Juventus and AS Roma in the group stage as Nice have it all to do in the return home leg in the Allianz Riviera stadium on August 22.
Spanish side Sevilla also set themselves up for a place in the group stage alongside Liga rivals Real Madrid, Barcelona and Atletico Madrid by beating Istanbul Basaksehir 2-1 in Turkey.
Franco-Tunisian forward Wisam Ben Yedder, picked up a backheeled pass from Jesus Navas, to seal the winner six minutes from time.
Sergio Escudero opened for Sevilla after 16 minutes with Eljero Elia getting the equaliser after 64 minutes.
A Scott Sinclair double helped Celtic to a 5-0 thrashing of Astana in their play-off round first leg in Glasgow.
An own-goal from Evgeni Postnikov opened the scoring in the 32nd minute before Sinclair doubled Celtic's advantage 10 minutes later.
The English winger then grabbed his sixth goal of the season on the hour before James Forrest added another in the 79th minute.
Leigh Griffiths rounded off the rout in the 79th minute with a deflection off Igor Shitov to help the Scottish champions secure a commanding advantage to take to Kazakhstan for the return leg next Tuesday.
"It was an outstanding team performance and the boys deserve a huge amount of credit. They managed the game very well," said Celtic manager Brendan Rodgers.
Elsewhere Hapoel Beer-Sheva beat Maribor of Slovenia 2-1 at home in Israel while Olympiacos beat Croatian side Rijeka by the same score in Greece.