Sterling pounced on a mistake after Arsenal centre-back David Luiz failed to clear a throughball by Kevin De Bruyne, steadying himself before smashing the bouncing ball past a helpless Bernd Leno shortly before half-time.
The goal was just reward for an industrious first-half display by Pep Guardiola’s side, who dominated the ball in typical fashion and created several promising openings.
It had been 100 days since the Premier League’s last goal after the top flight was put on hold due to the coronavirus pandemic.
Earlier in the evening, Sheffield United drew 0-0 at Aston Villa, having been denied a goal due to an error by goal-line technology.
The goal was Sterling’s 12th of the league season.