Chelsea were hammered 4-0 at Bournemouth in their last away league match and Maurizio Sarri's side were taken apart by the defending champions at the Etihad Stadium on Sunday, the Blues suffering their heaviest ever Premier League loss.
Raheem Sterling struck in the fourth minute and Ilkay Gundogan rapidly made it four after Aguero's first-half double, with Chelsea unable to muster any response in the face of City's incredible intensity.
Aguero, who also hit a treble in City's last home league game against Arsenal, stroked home a penalty after the break to join Alan Shearer on 11 Premier League hat-tricks and Sterling struck late to complete the scoring.
Pep Guardiola's side move above Liverpool on goal difference, with the Catalan coach enjoying a crushing victory against a side he has lost to on a record three league occasions.
City made a blistering start and led 4-0 inside 25 minutes, with Aguero on target twice.
Sterling opened the scoring with a thumping drive after Bernardo Silva's cross deflected into his path, then Aguero somehow missed an open goal from three yards out.
Aguero soon made amends with a thunderous 25-yard drive after great work from Oleksandr Zinchenko and he then capitalised on Ross Barkley's abysmal header to become City's record league goalscorer.
City's fourth came from Gundogan, his placed 20-yard shot beating Kepa Arrizabalaga, with Ederson brilliantly tipping over Gonzalo Higuain's volley at the other end before the break.
Aguero's header from Kevin De Bruyne's cross crashed against the crossbar but the Argentina attacker was able to celebrate his historic treble in the 56th minute.
Sterling's pace and skill drew a clumsy Cesar Azpilicueta foul inside the box and Aguero beat Kepa once more with an excellent penalty.
Guardiola was able to rest City's hat-trick hero, De Bruyne and Fernandinho for the closing stages and Sterling tapped in a cross from the lively Zinchenko for a simple sixth.
City send Liverpool a message
Goal difference might yet decide the title and, in thrashing Chelsea, City gave themselves an ever larger advantage over Liverpool. For the Blues, this was their fourth consecutive loss away from home in all competitions, with the aggregate score in their most recent three Premier League trips reading 12-0.
Silva's energy drives City forward
Aguero provided City's cutting edge and took his 2019 tally to 10 goals in all competitions, but the platform for their dominance was built on Silva's boundless energy. With namesake David surprisingly on City's bench, Bernardo was brilliant.
