The England winger curled in a precise finish from the edge of the area to open the scoring midway through the first half, with Jesus tapping home from a corner on the stroke of half-time.
Sterling headed home a third minutes before Bernardo Silva tapped in a rebound after Mat Ryan spilled his drive.
City’s No.7 then completed his hat-trick in slightly bizarre circumstances.
Brighton defender Adam Webster beat him in the air, but his header back to Ryan bounced off the falling Sterling’s head and through the goalkeeper’s legs to seal a comfortable victory.
Enjoy the five-star performance in the video above.