Amadou Diawara converted Napoli’s second PK after Dries Mertens saw his effort saved.
Napoli is six points back of Group F leading City, and three behind Shakhtar Donetsk.
[ MORE: Champions League standings ]
Raheem Sterling was near the spot to blast an open rebound past Pepe Reina in the ninth minute.
Then Kevin De Bruyne swept an incisive pass into the six for Gabriel Jesus to slot home, giving Man City a 2-0 lead in the 13th minute.
Kyle Walker saw yellow after giving a penalty kick in the 37th minute, and Napoli star Dries Mertens had his chance to pull one back denied by Ederson.
[ MORE: Full lineups, stats, box score ]
John Stones‘ impressive growth at City continued when he slid to stop Marek Hamsik from testing Ederson in the second half.
Fernando took down Faouzi Ghoulam to give Napoli a second penalty kick, and this time it was converted thanks not to Mertens, but Diawara.