On 18 minutes, City fashioned the first big chance of the half when Fernandinho directed a powerful header from a free-kick towards goal, forcing Kepa Arrizabalaga to tip the Brazilian's effort over the bar.
Ten minutes later, Chelsea threatened City for the first time, when Ross Barkley's cutback from the left by-line was met by Christian Pulisic at the near post, but his effort was scrambled away.
The Blues then opened the scoring against the run of play on 36 minutes when a mix-up between Benjamin Mendy and Ilkay Gündogan on the halfway line allowed Pulisic to nab the ball and fend off the retreating Mendy, before slotting past Ederson with ease.
City started the second half the stronger side again and ten minutes into the restart, they were level when Kevin De Bruyne scored a stunning free-kick from 22 yards which dipped over the Chelsea wall and beyond the scrambling Kepa into the top left corner.
From here, Chelsea looked rattled as City continued to pile on the pressure and they could have taken the lead not long after their equaliser, when Raheem Sterling found space in the box to turn and shoot, his effort curling just wide of the top right corner.
On 70 minutes, Pulisic had an effort impressively cleared off the line by a retreating Kyle Walker after the American had got behind the City defence and rounded Ederson.
Ten minutes later, Chelsea were awarded a penalty and City were reduced to ten men, when Fernandinho deliberately handled the ball on the line following Tammy Abraham's close range effort. Willian stepped up and confidently dispatched the penalty into the top left corner.
The final minutes saw City lose their rhythm, the visitors unable create any more chances as Chelsea held firm to secure a superb win that now sees them create some breathing space between themselves and Manchester United.
Takeaways from the match
Pulisic looked absolutely sensational tonight, causing City all sorts of problems with his runs round the back and tonight he proved his importance to the Chelsea squad, the Blues still hopeful in searching for the man that can replace Eden Hazard, however hard that may be.
Strength in depth
Man of the Match
Tonight's Man of the Match has to go to Christian Pulisic. His energy and tenacity tonight was fantastic and his goal showed just exactly what he is capable of in the moments that matter.
If he can keep up this kind of form, Chelsea will have themselves a superstar in the making.