Man City piled on the pain for Chelsea in the top four race, as Pep Guardiola's side leapfrogged the Blues to move up to fourth place on Saturday.
Chelsea fell to sixth after throwing away an early lead at the Etihad; Noni Madueke opened the scoring for the visitors after just three minutes.
Not long before half-time, City struck back when Josko Gvardiol notched an equaliser in the 42nd minute. Erling Haaland doubled the champions' lead in the second half, after a goalkeeping howler from Robert Sanchez.
As the Blues sought to level the affair, Phil Foden put the nail in the coffin, converting a one-on-one opportunity on a counter-attack late on.