Antonio Conte's side delivered an impressive statement of intent as they cut City apart on the break after going behind to Gary Cahill's own goal on the stroke of half-time, when he diverted Jesus Navas' cross beyond keeper Thibaut Courtois.
The game turned on Kevin de Bruyne's 56th-minute miss with City in control, crashing Navas' cross against the bar from inside the six-yard box.
Chelsea were level on the hour when Diego Costa outmuscled Nicolas Otamendi to score and they were ahead 10 minutes later when substitute Willian raced clear to beat City keeper Claudio Bravo with ease.
Eden Hazard completed a magnificent win for Chelsea with another goal on the break, showing too much pace for Aleksandar Kolarov to wrap up three vital points.
Source: BBC Sports