Sergio Aguero finished superbly in the first half before a Vincent Kompany header and powerful Fernandinho strike secured all three Barclays Premier League points.
City completely outplayed their rivals, piling on the problems for Jose Mourinho’s winless side after a difficult week dominated by the manager’s row with two of his medical staff.
There was further controversy as striker Diego Costa tried to confront Fernandinho at half-time following an on-field collision and had to be held back.
But for City, whose manager Manuel Pellegrini beat Mourinho for just the third time in 14 attempts, there were only positives.
They 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.