Sterling netted from 10 yards nine minutes into the game and Jesus from even closer range four minutes later, as the Citizens quickly clicked into gear.
After squandering chances to add a killer third, Amadou Diawara converted from the penalty spot - having seen Dries Mertens's earlier spot kick saved by Ederson - as the visitors set up a nervy finale.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Ederson; Walker, Otamendi, Stones, Delph; Fernandinho, De Bruyne Silva; Sane, Sterling, Jesus
SUBS: Bravo, Aguero, Gundogan, Danilo, Yaya Toure, Mangala, Bernardo
STARTING XI: Reina; Hysaj, Albiol, Koulibaly, Ghoulam; Diawara, Zielinski, Hamsik; Callejon, Insigne, Mertens
SUBS: Allan, Jorginho, Maggio, Maksimovic, Ounas, Rog, Sepe
Pep Guardiola: "Do I believe [Laurentiis]? Absolutely not. But he is travelling with Sarri in the same plane, or in a private jet. He can ask him, Mr Sarri, if he is going to play like this, but I think in the last eight games they played in the same lineup. I can announce which players are going to play, Napoli, against us. They do many many things and all the things they do they do perfectly. In Italy they have won eight games in a row, and won in Rome against Lazio and Roma."
Maurizio Sarri: "The feeling I get watching Man City play, I didn't even get watching Real Madrid last year. I always felt my team could give opponents a hard time, but this time I think Man City are a formidable team. But if we want to play at a certain level, we have to do it in important matches and aim at achieving results. I watched a few matches. I didn't want to watch all of them because I didn't want to get depressed. I think Man City are by far the strongest team in Europe at the moment."
MANCHESTER CITY SUBS: Bravo, Aguero, Gundogan, Danilo, Yaya Toure, Mangala, Bernardo
NAPOLI SUBS: Allan, Jorginho, Maggio, Maksimovic, Ounas, Rog, Sepe