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.
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.
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.
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.
- Napoli win 2-0 with disputed penalty as Nice finish with nineThe Indian Express
- Napoli 2-0 Nice: Dries Mertens and Jorginho strike before French side have ...Daily Mail
- Napoli takes first leg over Nice in Champions LeagueToronto Star
- Celtic equal record as Sevilla, Napoli close on group stageUEFA.com
- Champions League Review: Mertens stars as Napoli put two past NiceGoal.com
- Napoli beat Nice in UCL playoff first leg; Celtic thrash Astana, Sevilla winESPN FC
- Napoli punish nine-man Nice; Celtic winGulf Today
- Napoli beats 9-man Nice 2-0, closes in on Champions LeagueNew Zealand Herald
- Favre: 'We still have hope'LFP