Raheem Sterling put City ahead in the ninth minute, finishing with his left foot after Kyle Walker’s attempt to convert a David Silva pull-back was blocked.
Four minutes later, the in-form Kevin De Bruyne created the second, powering down the right flank and delivering a pinpoint low cross to Gabriel Jesus, who made no mistake.
Belgian midfielder De Bruyne fired a long-range shot against the bar in the 25th after a swift City counter-attack and then Jesus had a goalbound effort cleared off the line by Kalidou Koulibaly.
Napoli had an opportunity to narrow the deficit in the 38th minute after Kyle Walker gave away a penalty but City’s Brazilian keeper Ederson produced a fine save to keep out Dries Mertens’ kick.
The Italians were given a second chance from the spot in the 73rd minute, this time Amadou Diawara firing home after Faouzi Ghoujlam was tripped by Fernandinho.
Despite some late pressure from Maurizio Sarri’s side, City held on to secure their third straight win and leave them on top of the group with nine points. Napoli are third on three points, three behind second-placed Shakhtar.