Victory against the soon-to-be-deposed Premier League title-holders came just days after City reached the semi-finals of the Champions League by knocking out fellow big-spenders Paris Saint-Germain.
Aguero was aided repeatedly by the excellent Kevin De Bruyne, with the former Chelsea midfielder impressive on his first Premier League return to Stamford Bridge.
The Belgian played a key part in two of Aguero's goals either side of half-time before the Argentina striker completed his treble with an 80th-minute penalty following an incident that saw Chelsea goalkeeper Thibaut Courtois sent off.
This commanding performance saw City leapfrog Arsenal into third place, although the Gunners will regain that position if they beat Crystal Palace in Sunday's all-London clash at the Emirates Stadium.
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More importantly, it also kept City four points clear of fifth-placed local rivals Manchester United, with only the top four clubs in the Premier League at the end of the season qualifying for the Champions League.
For Chelsea, this was the latest dispiriting result in a season that has left them 10th in the table and, coming after a defeat by Swansea last time out, it meant caretaker boss Guus Hiddink had lost two league games in a row as a club manager for the first time since February 2004, when the Dutchman was at PSV Eindhoven.
City started as if they had still to get Tuesday's 1-0 win over PSG out of their system.
Nicolas Otamendi struggled with a ball forward in just the fifth minute, letting Diego Costa in for a chance. Joe Hart did well to force the striker back and, once the ball fell to Pedro, Otamendi redeemed himself to clear the winger's effort off the line.
City looked chaotic at the back for most of the opening 20 minutes, as Ruben Loftus-Cheek and Gary Cahill both went close, until De Bruyne -- who scored against PSG on Tuesday -- finally provided a spark for the visitors.
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Played in by Yaya Toure, he burst forward in the 23rd minute only for his Belgium team-mate Courtois to stand up well and divert his shot wide.
Courtois, however, was helpless to prevent City taking the lead 10 minutes later.
De Bruyne's pace again took him clear of the Blues' defence and, this time going down the right, he squared for Aguero.
The Argentinian steadied himself before, looking to curl the ball around Courtois, his shot deflected off Cahill and found the corner of the net anyway.
On the resumption of the second half, Chelsea again started strongly, only to be caught on the break.
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De Bruyne was once more at the heart of the move. He embarrassed Cesc Fabregas with a devastatingly swift turn, playing the ball on for Samir Nasri, who set up Aguero's second goal of the game.
Chelsea were again unable to cope with the sheer speed of a City counter-attack in a move that led to the visitors' third 10 minutes from time.
Fernandinho was put through for a one-on-one with Courtois, only for the goalkeeper to bring him down.
The Belgian was already walking off the pitch before referee Mike Dean showed him the red card, and Aguero then beat substitute goalkeeper Asmir Begovic from the spot to complete his hat-trick.
City were a team transformed from the side that had started in such sluggish fashion and, on this evidence, Spanish giants Real Madrid won't have it all their own way when they meet Pellegrini's men in the last four of the Champions League.
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