With Sergio Aguero playing for the first time in almost four months, City seemed to begin with a spring in our step - having the first effort on goal within just 50 seconds, with Riyad Mahrez curling just wide.
Aguero was straight into the thick of the action, finding space in the box but directing his header over the bar from a Mahrez cross.
Sterling, who was the skipper on the night, broke the deadlock in the 23rd minute, firing in a rebound with his left foot after Phil Foden's low effort was parried back out by Bernd Leno.
The Englishmen were a constant nuisance for the Arsenal back-line, linking superbly with Aguero, Mahrez and Bernardo Silva on multiple occasions, with Foden coming closest to adding a second, but he was well denied by Leno when through on goal.
Mikel Arteta's side looked to hit back before the interval, but found Ederson in inspired mood, saving expertly from Bukayo Saka twice.
It was a cagey second period under the floodlights, but Guardiola's men remained alert defensively and saw out the victory to confirm a perfect return from the international break.
View the best images from the tense affair via our gallery below.