Sterling himself weighed in with a fine brace of goals with Ilkay Gundogan also on target as City served up a stunning all-round display to leapfrog Liverpool and go back on top of the Premier League on goal difference.
Aguero became City's all-time record league goalscorer, his treble taking him to 160 goals.
It also saw the Argentine – who is the Club's al-time leading goalscorer - draw level with Alan Shearer with 11 Premier League hat-tricks.
“Sergio is a player we depend on," Sterling reflected after the full-time whistle.
“You saw with his first strike putting the ball in the top corner - you have to cherish players like that.
"It was a terrific performance from the team - the manager set us up and got us ready for the game.
"It was just a win and another three points. The most important thing is to get three points."