Sterling made six starts in England's semi-final run at the 2018 FIFA World Cup and only returned to training with City on Tuesday (NZST) last week.
He rewarded Pep Guardiola's faith with a lively showing and a clinically dispatched 14th-minute opener.
The first game of Arsenal's new era under Unai Emery often proved a thankless task but there were moments of encouragement before Silva settled the issue with a brilliantly taken second in the 64th minute.
Petr Cech — preferred in the Arsenal line-up to new arrival Bernd Leno — saved sharply at his near post in the ninth minute after Sterling twisted past Shkodran Mustafi.
But the veteran goalkeeper was grasping at fresh air when Sterling sashayed inside to lash home a shot from the edge of the box.
Hector Bellerin gave Ederson his first serious task in the City goal but that Arsenal foray only led to a swift counter-attack that ended with Sergio Aguero testing the side-netting.
Cech bailed out his ailing team-mates by thwarting Aymeric Laporte at point-blank range having parried Riyad Mahrez's free-kick.
Guardiola responded to Arsenal pressure early in the second half by sending on Kevin De Bruyne with half an hour remaining and the Belgium midfielder was furious to be denied the chance of doubling City's lead.
Matteo Guendouzi's error gave Aguero the freedom of the Arsenal half and the Argentina star shot too close to Cech as De Bruyne screamed for a square pass.
The anguish did not last long as Benjamin Mendy made his way to the byline and cut the ball back for Silva to find the top-left corner emphatically.
Pierre-Emerick Aubameyang had a goal ruled out for offside and blazed over at close quarters as late lethargy brought errors into City's game, something that will not have escaped its perfectionist manager.
The tough assignments keep rolling in for Emery, with a short trip to Stamford Bridge next weekend, while City faces a Huddersfield Town team that has already suffered at the hands of "Sarri-ball".