City fans couldn't have asked for a better opening 45 minutes from their side with Sterling opening the scoring after eight minutes before Jesus added a second five minutes later, it should have been three and then four when Kevin De Bruyne clattered the underside of the crossbar and Kalidou Koulibaly cleared off-the-line before Ederson saved Dries Mertens' penalty.
The visiting Italians started to pick up their form in the second period with Marek Hamšík's effort been blocked before Amadou Diawara buried their second spot-kick, but it wasn't enough to stop the Citizens continuing their perfect start.
Kicking it off with some style
The clash at Etihad Stadium brought in arguably the two most entertaining sides on the continent, both have been in excellent form and the home side continued that very early on.
They certainly weren't dropping the tempo from Saturday's 7-2 drubbing of Stoke City as Leroy Sané found the run of skipper David Silva to the byline, the Spaniard picked out the unmarked Kyle Walker whose effort was blocked but Sterling was there to turn home at the second time of asking.
It didn't take too long for the home side to double up their lead, De Bruyne has been in fine form and was it at it again as he was the first to a defensive header. The Belgian played a curling effort into the mixer and it was easy enough for Jesus to tap home.
Should have been four
De Bruyne could have made it one better as he clattered the woodwork in the 24th minute, Sané received the ball from Sterling as the German rolled it back to the Belgian whose effort had Pepe Reina beaten but he was saved by the crossbar.
City were proving ruthless inside the opening half hour and could have ended it minutes after De Bruyne clattered the crossbar, it was superb as Silva dinked it over to Sterling who volleyed it into the danger zone. It came to Jesus who managed to get the shot away on the swivel, but Koulibaly was there to eventually clear.
Just not their night
Napoli had been very much under quash throughout the majority of the first period, but were handed an avenue back into the clash when they were handed a penalty.
It was poor from Walker as he blatantly pulled down Raúl Albiol at the corner and Antoinio Mateu Lahoz had no hesitations in pointing to the spot, Mertens looked certain to bury it but it was straight down the middle from the Belgium and Ederson easily blocked with his legs.
Making it interesting
Guardiola's side looked to have taken their foot off the gas slightly at the beginning of the second period, which allowed the Italians to eventually get back into the contest.
Their best chance from open play came in the 64th minute as Mertens did well to beat Ederson to the ball and square it to Hamšík, the Serbian had the goal gaping but John Stones was there to block the effort.
City' defence didn't seem to learn their lesson from the first period as they gave away another penalty, Faouzi Ghoulam did well to run at the hosts defence before been brought down by Fernandinho. Diawara was penalty duties this time around and made no mistake as he buried into the bottom corner.
The City contingent inside the Etihad Stadium will have thought they had breathing space as Jesus rounded Reina and slotted home, but the Brazilian's celebrations were cut short as the flag was raised for offside.