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.
TWEET OF THE MATCH
"Well, that near faultless performance by @MCFC has set the standard for all the other teams in the @premierleague" - Former Chelsea defender Graeme Le Saux (@graemelesaux14) was impressed by Manchester City
https://twitter.com/graemelesaux14/status/632959719620104192
PLAYER RATINGS
Manchester City:
JOE HART: Seven out of 10.
BACARY SAGNA: 7
ELIAQUIM MANGALA: 8
VINCENT KOMPANY: 8
ALEKSANDAR KOLAROV: 9
FERNANDINHO: 8
YAYA TOURE: 9
RAHEEM STERLING: 8
DAVID SILVA: 9
JESUS NAVAS: 8
SERGIO AGUERO: 9
Substitutes:
SAMIR NASRI: 7
MARTIN DEMICHELIS: 7
WILFRIED BONY: 6
Chelsea:
ASMIR BEGOVIC: 7
BRANISLAV IVANOVIC: 4
JOHN TERRY: 5
GARY CAHILL: 4
CESAR AZPILICUETA: 6
NEMANJA MATIC: 5
RAMIRES: 6
WILLIAN: 5
CESC FABREGAS: 5
EDEN HAZARD: 4
DIEGO COSTA: 4
Substitutes:
KURT ZOUMA: 5
JUAN CUADRADO: 4
RADAMEL FALCAO: 4
STAR PLAYER
Yaya Toure: Infuriated both sets of fans at times with his play-acting, but when he was not rolling about on the floor, the big Ivorian was unstoppable, both on the attack and in defence
Chelsea's midfield usually looks solid, but they had no answer to Toure's bustling runs.
MOMENT OF THE MATCH
When the new Chelsea medical team took to the pitch for the first time in the 44th minute to treat Gary Cahill
The City supporters took to their feet and applauded sarcastically before shouting: "You're getting sacked in the morning!" They also chanted "Eva! Eva! Eva!" in support of demoted doctor Eva Carneiro.
VIEW FROM THE BENCH
Jose Mourinho opted to field Ramires instead of Oscar to give Branislav Ivanovic some protection from Raheem Sterling and Aleksandar Kolarov, but the tactic did not work as City flung in cross after cross from the left
The defeat showed Chelsea's lack of strength and variety
The Chelsea boss tried to change the game by bringing on Juan Cuadrado but he had no impact.
MOAN OF THE MATCH
Diego Costa's tantrum
The Spain striker made a beeline for Fernandinho as the teams walked off the pitch at half-time and had to be restrained by two Chelsea team-mates and two coaches
The midfielder did catch Costa with a flailing arm, but the striker seems incapable of letting things go and he was lucky to avoid being sent off
His tenacious style on the pitch has its advantages, but the lack of discipline will cost Chelsea dearly this season.
WHO'S UP NEXT
West Brom v Chelsea (Premier League, Sunday 23 August)
Everton v Man City (Premier League, Sunday, 23 August)
Source : PA
Source: PA