The Argentina international scored two of City's four goals in the opening 25 minutes and then rounded off his 11th top-flight treble before the hour, equalling Alan Shearer's long-standing record for the number of Prem hat-tricks.
Raheem Sterling started the scoring early on and rounded it off at the end, while Ilkay Gundogan was also on target for the Citizens as they cruised to a win that lifts them back above Liverpool on goal difference, albeit having played a game more than their title rivals.
It took a little under four minutes for City to make the breakthrough, catching their opponents out with a quick free kick.
Kevin De Bruyne released Bernardo Silva down the right and the Portuguese's cutback deflected off David Luiz into the path of an unmarked Sterling, who thumped the ball past Kepa Arrizabalaga from 10 yards.
Then, shortly after being guilty of a miss of the season contender when failing to convert from three yards at the back post, Aguero guided the ball past Kepa from 20 yards further back for his first of the afternoon.
Chelsea were again the victims of their own downfall for City's third as Luiz half-cleared the ball to Ross Barkley, who headed it back to where it came from.
Aguero pounced and sent a first-time shot past a stranded Kepa to all but seal the points for the champions with less than a quarter of the game played.
The fourth goal would arrive soon after, again following some sloppy defending as Aguero and Sterling exchanged passes in the box, before Antonio Rudiger cleared the ball to Gundogan to curl the ball into the net from outside the box.
Having conceded four goals in the first half of a Premier League match for the first time since December 1999, Chelsea temporarily grew into the contest, though that was mainly because City allowed them to do so.
Ederson produced a couple of saves to keep out Pedro, the first of which came with the Spaniard through on goal after being played in by Gonzalo Higuain, before then getting a hand to Higuain's long-ranger to keep his clean sheet intact.
Only once before in Premier League history has a side recovered from four goals down at the break to salvage a point - Newcastle United against Arsenal in 2011 - and Chelsea's task became even more difficult early in the second half.
Aguero struck the crossbar with a header, but he made no mistake from the penalty spot - after Cesar Azpilicueta hacked down Sterling - to score his landmark hat-trick.
De Bruyne then had a free kick punched clear by Kepa and Fernandinho was also thwarted from a similar range as the hosts toyed with their opponents.
City had the luxury of bringing on Gabriel Jesus for hat-trick hero Aguero, and the substitute striker was the next home player to come close to scoring when his low drive was saved by Kepa.
There would be a sixth goal before the end, though, with Sterling converting Oleksandr Zinchenko's left-sided cross in the final 10 minutes - a goal that sends the well-beaten visitors below Arsenal into sixth place on goal difference.
Chelsea, also thrashed 4-0 by Bournemouth in their last away outing, meet City again at Wembley Stadium in two weeks' time in the EFL Cup final.
MANCHESTER CITY XI (4-3-3): Ederson; Walker, Stones, Laporte, Zinchenko; Gundogan, Fernandinho (D.Silva 75'), De Bruyne (Mahrez 68'); Bernardo, Aguero (Jesus 65'), Sterling
CHELSEA XI (4-3-3): Kepa; Azpilicueta, Luiz, Rudiger, Alonso (Emerson 73'); Kante, Jorginho, Barkley (Kovacic 52'); Pedro (Loftus-Cheek 66'), Higuain, Hazard