In front of a record 54,331 attendance at the Etihad Stadium, Aguero opened the scoring with a sublime effort on 31 minutes, before captain Kompany doubled City’s lead with a well-guided header in the second half – the Belgian’s second goal in two games.
In a match that the home side thoroughly dominated, Brazilian midfielder Fernandinho – who had earlier angered Diego Costa with a flailing elbow – secured all three points with an excellent drive from 20 yards to send City to the top of the Premier League table.
Manuel Pellegrini’s men started superbly, hitting Chelsea with great pace in attack and defending with determination.
They might have taken the lead within a minute as David Silva set up Aguero but back-up goalkeeper Asmir Begovic saved superbly and Jesus Navas drove wide.
Aguero, making his first start of the season, looked sharp but was denied twice more by Begovic inside the opening 15 minutes and then poked wide from an Aleksandar Kolarov cross. Cesar Azpilicueta also had to clear over his own crossbar as City made all the running.
Chelsea wanted a penalty early on after Costa went down but had only half-chances for Branislav Ivanovic and Ramires before City took the lead.
Aguero took the 31st-minute opener brilliantly, wrong-footing Gary Cahill with a sharp turn and then calmly slipping the ball past Begovic.
The first half ended amid scenes of confusion and controversy, some farcical, some more serious.
Problems began as a Kolarov free-kick beat everyone but Cahill required treatment after being caught in the face by Begovic.
Until this point, Chelsea’s medics had been conspicuous by their absence but the sight of Steven Hughes and Chris Hughes running onto the field for the first time brought huge ironic cheers from the home fans.
They even chanted, “You’re getting sacked in the morning,” in a touch of humour following the apparent demotion of doctor Eva Carneiro and physio Jon Fearn.
But the mood darkened as Costa took an apparent elbow from Fernandinho. With Chelsea’s staff otherwise engaged, a City physio came on to bandage up the stricken Spaniard.
Costa was clearly riled and made an attempt to reach the Brazilian as the players left the field at half-time. He was restrained by a member of Chelsea staff but problems continued in the tunnel and TV pictures showed the striker being held back by coaches Rui Faria and Silvino Louro as well as team-mates Ivanovic and Ramires.
Chelsea’s inspirational captain John Terry was replaced by Kurt Zouma during the break as Mourinho tried to tighten up.
The game became scrappier as Chelsea tried to up the tempo with Eden Hazard coming more into the game and Ivanovic whipping in a dangerous cross.
City still threatened with Yaya Toure testing Begovic and Aguero firing wide but needed Joe Hart to save them as Hazard worked a fine chance in the area.
They then wrapped up the points as Kompany headed home from a Silva free-kick 11 minutes from time and Toure set up Fernandinho six minutes later.