Despite dominating long periods of the first-half, the Blues were undone by the hosts’ first shot on target on the stroke of half-time and a second late in the game.
It was the champions’ first loss of the season and it also means Liverpool replace the Blues as Premier League leaders.
City started as they meant to go on and hared after every ball, closing Chelsea down and forcing errors from the hosts who struggled to cope with the intensity and energy the champions were showing.
With just eight minutes played, Raheem Sterling had a guilt-edged opportunity as Leroy Sane’s cross found the England forward near the penalty spot, but his weak shot was easily saved.
Sterling again broke free on the edge of the box seconds later but was caught in two minds as Chelsea clung on for dear life.
The Blues were hungrier and better in every department at that stage, and on 15 minutes, another good chance was spurned as a combination of Sane, Mahrez and Bernardo ended with Sane delaying his shot a fraction too long and Chelsea scrambling the danger clear.
It was frantic, non-stop edge-of-the-seat stuff.
Sane was causing all kinds of problems in the left and City again went close as the German winger found himself in space in the box after wonderful skill by Sterling, but Azpilicueta threw himself in the way of the ensuing shot to save his team.
The one worry was that the Blues would be made to pay for the chances missed and, so it proved a minute from the break.
David Luiz’s long cross-field ball seemed to catch City cold and with defensive lines exposed for once, Eden Hazard was able to play a shot ball into space where N’Golo Kante was on hand to fire Chelsea’s only shot of the half into the roof of the net.
That the Blues went into the break behind was harsh, but it was the price of not taking at least one of three excellent opportunities.
With their tails up, Chelsea showed more intent after the restart and only an excellent save from Ederson as he beat out a Willian free-kick on 47 minutes to keep City in the game.
Gradually, the Blues regained their composure and forced a series of corners before Kyle Walker saw a free-kick beaten out by Kepa.
City started to build up a head of steam, with Sterling and sub Gabriel Jesus working hard to find a way through the home defence, but on 77 minutes, the contest was effectively ended as Luiz headed home from what had been a disputed corner.
Not a good day for the champions who didn’t deserve to leave Stamford Bridge empty-handed, but those early misses ultimately proved costly.
What it means?
The Blues have slipped to second in the Premier League, a point behind Liverpool.
The champions are back in action on Wednesday evening with the final Group F game against Hoffenheim.
Then it’s back to Premier League action at home to Everton next Saturday with a lunchtime 12.30pm kick-off.