City struck twice in the opening 13 minutes at the Etihad Stadium to set themselves up for a result that lifted them six points clear of the Serie A leaders, and their supposed chief rivals, in Group F.
Napoli hit back strongly with Dries Mertens having a penalty saved before Amadou Diawara did score from the spot, but City survived a nervy finish.
John Stones believes City came through a “tough test,” pointing out: “I think tonight was a great test to see where we were really at after a good run of hard games. We knew it was going to be a tough test.
“We wanted to play our game and I think some of the football out from the back right the way through to the guys up top was, at times, great to watch for me personally.
Pep Guardiola’s men arguably should have put the game beyond reach in the opening half-hour, as Kevin De Bruyne also hit the bar and Jesus was denied a second on the line.
Buoyed by their 7-2 thrashing of Stoke at the weekend, they were quickly into their stride.
Their first goal came after Leroy Sane opened up the Napoli defence and Sterling turned in a low shot after Kyle Walker’s initial effort was blocked.
De Bruyne continued his rich vein of form by creating the second just moments later, seizing on a loose ball and delivering a now typically perfect pass into the path of Jesus.
The Brazilian made no mistake from close range.
City had goalkeeper Ederson to thank for preserving their lead.
The Brazilian first did well under pressure from Jose Calleron to claim a dipping cross from Lorenzo Insigne.
He then beat away Mertens’ spot-kick after Walker was adjudged to have felled Raul Albiol, and also dealt with a long-range shot from the Belgian.
Mertens was frustrated again before the break as Nicolas Otamendi blocked another powerful effort.
Considering their exhilarating start, City had gone off the boil as the half-time whistle was blown.
De Bruyne tried to voice some grievance to the officials as he left the field and he reacted angrily as team-mates Fernandinho and David Silva pushed him away.
Napoli continued to make their presence felt after the break. Jesus broke clear only to be halted by a fine tackle from Albiol.
Marek Hamsik - one short of equalling Diego Maradona’s Napoli goalscoring record - was denied by a brilliant sliding block from John Stones after Fernandinho had lost possession.
They were awarded a second penalty after 73 minutes when Fernandinho brought down Faouzi Ghoulam. Diawara grabbed the ball this time and placed a fine shot into the bottom corner.
City went close again as Napoli goalkeeper Jose Reina saved a De Bruyne free-kick and a Sane shot, but the hosts were relieved to hear the final whistle.
Ederson, Walker, Stones, Otamendi, Delph, De Bruyne, Fernandinho, Silva (Gundogan 76), Sterling (Bernardo Silva 69), Gabriel Jesus ( Danilo 86), Sane.
Reina, Hysaj (Maggio 70), Albiol, Koulibaly, Ghoulam, Zielinski, Diawara, Hamsik (Ounas 78), Callejon, Mertens, Insigne (Allan 57).
Antonio Miguel Mateu Lahoz (Spain).