Aguero should have had even more than three as the Argentine missed a glorious early chance and hit the bar in the second-half in a humiliating afternoon for Maurizio Sarri's men.
Raheem Sterling started and ended the scoring and Ilkay Gundogan also netted in the first quarter of the game as City ended what could have been a testing week with a trip to Everton in between the visits of Arsenal and Chelsea with maximum points.
Jurgen Klopp's men maintain the advantage of a game in hand, but handed a reprieve by Liverpool's draws against Leicester and West Ham in recent weeks, City look determined to become the first side in a decade to retain the Premier League.
Chelsea on the other hand slip to sixth with the scale of the defeat sure to raise further doubts over Sarri's future. A 4-0 defeat to Bournemouth in their last away game was Chelsea's heaviest league defeat since 1996.
And this was their worst loss in any competition since 1991 after failing to recover from Raheem Sterling's fourth-minute opener.
Eden Hazard went to sleep from Kevin de Bruyne's quickly taken free-kick and Bernardo Silva had acres of space to cross for the England international to fire home.
"We conceded the goal after four minutes in a stupid way," added Sarri. "At that moment we had to only stay in the match and we were not able to stay in the match because we made a lot of mistakes against the wrong opponents. They played really fantastic football today."
Liverpool maintain the advantage of a game in hand over City, but given a reprieve by draws for Jurgen Klopp's men against Leicester and West Ham in recent weeks, the champions look determined to become the first side in a decade to retain the Premier League.
"My feeling is it is going to finish in the last games. The important thing, after what we have done last season, is being there," said City boss Pep Guardiola.
"Normally people fall down after what we have done last season but we are still there."