The narrow winning margin flattered the defending champions, who did not register a shot on target in an uambitious smash-and-grab attempt from Antonio Conte.
Having seen how Pep Guardiola's side twice put Arsenal to the sword this week, Chelsea were very defensive in their approach and were more than content to sit off the hosts.
Two of City's goalscorers at the Emirates Stadium on Thursday - Leroy Sane and Bernardo - combined to set up the latter for a curling shot which glanced the roof of the net on 21 minutes.
Sane was City's biggest threat and he came close to giving the hosts the lead before the half-hour mark when he worked a deep free kick from Kevin De Bruyne back onto his right foot and shot past Thibaut Courtois, only for Cesar Azpilicueta to clear off the line.
For the first time since Opta records began in the 2003-04 campaign, Chelsea failed to register a single attempt on goal during the first half, with an isolated and frustrated Eden Hazard living off little service.
Chelsea's plan to keep out City was undone immediately after the restart when a miscued clearance from Andreas Christensen fell to Sergio Aguero, who teed up David Silva for a cross which Bernardo turned home at the far post.
For a brief 10-minute spell, the Blues showed signs of life and created their one and only clear-cut chance when Fabregas released Victor Moses, who sliced his shot wide of Ederson's goal from a tight angle.
The hosts responded by quickly wrestling back control of the game but they were unable to put Chelsea away as Courtois stood firm at his near post to push away Silva's shot after a driving run from the Spaniard.
Chelsea's cautiousness made it difficult for the Citizens to replicate their fluency from the Arsenal double header, and the Blues did take the contest the distance despite never getting their own attacking game going.
Conte waited until the 78th minute to introduce Olivier Giroud, and threw on Alvaro Morata with only a minute to go, although a hopeful hook from the Spaniard nearly set up a stoppage-time Chelsea sucker-punch as Marcos Alonso sliced a volley wide.
A five-point gap to Tottenham Hotspur leaves Chelsea with a lot of work to do to make the top four, while City are now 18 points clear at the top of the table and one step closer to an emphatic title triumph.
MAN CITY (4-3-3): Ederson; Walker, Laporte, Otamendi, Zinchenko (Danilo, 87'); Gundogan, Silva (Foden, 90'), De Bruyne; Bernardo, Sane, Aguero (Jesus, 85')
CHELSEA (5-4-1): Courtois; Azpilicueta, Christensen, Rudiger; Moses, Fabregas, Drinkwater, Alonso, Willian (Giroud, 78'), Pedro (Emerson, 82'); Hazard (Morata, 89')