Named skipper for the day, the England winger struck a fine 24th minute effort to ensure Pep Guardiola’s side overcame the challenge of a tenacious and dogged Gunners.
It was Sterling’s fourth goal of the season and capped a satisfying night’s work for City with all-time leading scorer Sergio Aguero back in action for the first time in four months after his knee injury.
Though Pep Guardiola went into the fixture with an impressive Premier League record against the Gunners, City also kicked off seeking a measure of revenge for last July’s FA Cup semi-final loss to the Gunners.
The impact of former City assistant manager Mikel Arteta on Arsenal since he took charge was clear to see that day and the visitors looked to deploy a similar approach this time as he they sought to harry and press.
City were buoyed by the welcome return to action of Sergio Aguero, who was back in action after almost four months on the side-lines with a knee injury.
And within 60 seconds of kick-off we illusrated our attacking intent as Riyad Mahrez rounded off a sweeping attacking move by curling a superb shot just wide.
Bernardo Silva, who was also making his first start of the season, was deployed centrally and a real livewire presence in the early stages as he probed Arsenal’s back line.
But just as Arsenal were growing in confidence, our attacking instincts were rewarded on 24 minutes as we took the lead through skipper for the day Raheem Sterling.
Sterling showed his awareness and anticipation by latching on to rebound drilling home his fourth goal of the season.
The visitors sought an instant response and Ederson needed to be alert to keep out a Bukayo Saka effort before Pepe flashed a header wide.
With the intensity stepping up, Leno then did well to get low and deny Mahrez after the Algerian had drifted inside and looked to beat the keeper at the near post before the winger then whistled another effort just over.
Another superb piece of vision by Aguero then put Foden in on goal after Cancelo had intercepted an Arsenal clearance but Leno denied the England youngster by rushing out to block his goalbound effort.
In what was a pulsating clash Ederson was next to earn his goalkeeping spurs, the Brazilian making a crucial save to push Saka’s shot just wide after Arsenal had pierced the City defence.
And as a breathless first half ended Arsenal appealed in vain for a penalty after a Walker challenge with Gabriel Magalhaes.
Mahrez then tested Leno's reflexes again early in the second half as City sought that crucial second goal.
At only 1-0 up, it meant the game was balanced on a knife-edge and City were grateful to see a David Luiz free-kick sail over after Dias had impeded Pepe on the edge of the box.
That second goal almost arrived on 76 minutes after some dazzling skill from Cancelo twisted Arsenal inside out. The Portuguese star, who had impressed in a midfield role, drilled in a low cross with struck Luiz but rolled inches wide of the target.
And City were relieved to see a dangerous in-swinging Luiz cross just evade the leaping Aubameyang with the clock ticking down.
However, City held our collective nerve to secure a valuable three points and our second league win of the season.
Man of the match
Raheem Sterling proved a thorn in Arsenal's side all afternoon and capped a fine performance by claiming the winner.
It was the England forward's fourth goal of the season - and he had already illustrated he is in the mood to try and emulate last term's formidable goal-scoring exploits.
And his impact was further illustrated by the fact he was captain for the day.
Arsenal: Leno, Bellerin, Holding, dos Santos, Tierney, Ceballos, Xhaka (Partey), Saka, Willian (Lacazette 68), Pepe (Nketiah 82), Aubameyang
Subs: Lacazatte, Runarsson, Maitland-Niles, Partey, Luiz, Elneny, Nketiah
What it means
The victory moves City up into 10th place in the table on seven points from our first four games, with a crucial game in hand on most of our rivals.
City are back at the Etihad on Wednesday when we begin our 2020/21 Champions League campaign at home to Porto. Kick-off is 8pm.
We then resume Premier League action away at West Ham next Saturday with kick-off at the London Stadium slated for 12.30pm.