Sterling popped up in the box after just two minutes as Riyad Mahrez scooped a cross to the back post for the England international to head home.
Mohamed Elneny came within inches from equalising after 70 minutes as the Egyptian almost capitalised on a sloppy mistake from Ederson, but City were let off the hook and closed out the game to narrowly win by a single goal.
Quick out the blocks
Sterling opened the scoring with just two minutes on the clock - the single moment of magic that inevitably decided the game. The goal made it nine in the league and 13 in all competitions for Sterling, who is coming back into form at the right time.
Kevin De Bruyne and Joao Cancelo came the closest throughout the rest of the game, but they could not extend the lead for City, meaning the Citizens were kept on the edge of their seats for the majority of the game.
Luckily for them, the Gunners were unable to take their clear-cut opportunities to draw level, which meant City managed to take all three points to continue their winning run.
100 for Stones
Sunday night's ground-out win against Arsenal marked 100 Premier League appearances in a City shirt for John Stones. Although a quiet night in general for the City defence, there was still a job to do and the Englishman stuck to the task throughout.
It also meant that the trio of Ederson, Stones, and Ruben Dias are still yet to concede a single goal from open play so far this season. They have started 14 games together, spanning over 1250 minutes without an open play goal given up.
With his recent run in the side and spectacular form with City, a place in England's Euro 2020 team could be in his sights alongside the likes of Harry Maguire, Connor Coady, and fellow Citizen Kyle Walker.
Despite Sterling's header early on, the strikers for both sides had a quiet game on the night.
Pierre-Emerick Aubameyang was up against the tightest and toughest centre-back partnership in the league and had little to no support around him. As a result, it was little surprise to see him struggle.
City were without a recognised striker for yet another game, with the front three consisting of Mahrez, Sterling, and Bernardo Silva on this occasion.
Pep Guardiola brought Gabriel Jesus on to end the game once and for all, but even the Brazilian did not have his shooting boots on as he smashed a couple of chances over the bar to frustrate the Blues' manager.
The perfect captain
Fernandinho boasted the highest player rating on the pitch, even bettering goalscorer Sterling.
Despite only starting six Premier League games so far this season, the club legend controlled the pitch as if he had never left - like a duck to water.
“He’s the perfect captain on and off the pitch. When we were in a bad run, he called a meeting in the changing room and we spoke how things were going wrong and how it could go better - and since then we’ve improved."
"He is a captain even when he doesn’t play as much as he wants to,” said Phil Foden in a recent interview with BBC.