The visitors, who were without a number of first-team players following an outbreak of coronavirus at the club, stunned Lampard’s side with three goals in the space of 16 first-half minutes.
Ilkay Gundogan’s crisp low finish broke the deadlock before Phil Foden doubled City’s lead three minutes later, tucking a superb first-time strike beyond Edouard Mendy after fine work from Kevin de Bruyne.
The Belgian then deservedly got his name on the scoresheet with a close-range finish after Raheem Sterling’s curling strike had rebounded off the woodwork.
Callum Hudson-Odoi scored in second-half stoppage time for Chelsea, firing Kai Havertz’s cross beyond Premier League debutant Zack Steffen.
The result lifts City up to fifth in the table, four points off Liverpool and Manchester United, and with a game in hand on both their rivals.