Manchester City moved back to the top of the Premier League after humiliating a stunned Chelsea 6-0 at the Etihad on Sunday.
Aguero scored his third on 56 minutes from the penalty spot to make it a record 11 Premier League hat tricks in total, level with Alan Shearer. Sterling finished things off 10 minutes from time as Chelsea suffered their heaviest ever Premier League defeat.
The glut of goals also boosted City's goal difference, with the champions leapfrogging Liverpool to go top as well as moving 10 goals clear of their closest challengers in second.
For Chelsea boss Maurizio Sarri, further questions over his future will be asked following a gutless display. Plenty of travelling fans had left their seats long before the full time whistle, with Sarri left to pick up the pieces following another embarrassing defeat hot on the heels of a 4-0 loss at Bournemouth on Jan. 30.
The rout started on four minutes when Marcos Alonso fell asleep at a free kick and the ball eventually found its way to Sterling, who slammed in. Aguero then inexplicably missed an open goal from point blank range to the total bemusement of the Etihad, but he soon made amends in style. Collecting the ball around 25 yards out, Aguero unleashed a superb effort that sailed into the top corner to put City well in control.
Aguero then profited from Ross Barkley's glaring error to slip the ball home to make it three. There seemed little danger when Barkley had the chance to clear but his header back to Kepa Arrizabalaga was weak and Aguero pounced. With Chelsea reeling, City deepened the misery on Sarri's men on 25 minutes when Gundogan sent a drive of his own goalwards and Kepa had no answer.
There was no let-up in the second half as Aguero thudded a header against the bar five minutes after the restart, with City showing no signs of slowing down following their first half masterclass.
Chelsea, for all their faults at the back, showed flickers of promise in attack with Gonzalo Higuain forcing Ederson into a fine save amid the first half barrage and linking well with Eden Hazard at times.
It got worse for the visitors, though, when Cesar Azpilicueta tripped Sterling in the area and Aguero stepped up to coolly slot home the fifth for a rampant City on 56 minutes.
Aguero, whose 160 goals make him City's leading scorer in league football, was replaced on 64 minutes for Gabriel Jesus and Kevin De Bruyne soon followed to be replaced by Riyad Mahrez as Guardiola rested his stars with the job well and truly done.
There was still time for Sterling to grab his second, finishing off a fine passing move inside the area as City scored their 120th goal of the season -- the most across Europe's top leagues.