City were 4-0 up after 25 minutes, with Raheem Sterling slamming home before Aguero smashed in from 30 yards.
Aguero prodded home when Ross Barkley misplaced a header and Ilkay Gundogan struck from 18 yards before the break.
The Argentine – who missed from two yards moments before his eye-catching first goal – also became Manchester City’s all-time leading league goal scorer in the process, moving to 160 goals to surpass Eric Brook on 158.
City now sit top of the Premier League courtesy of a nine-goal superior difference over Liverpool, who have a game in hand.
Chelsea, who had not lost a competitive game so heavily since 1991, are sixth, a point off the Champions League qualification places.