And with manager Stuart Pearce's job apparently on the line, his players produced a battling display against the current Premiership champions.
City made Chelsea scrap hard for their narrow victory which was secured through a first-half penalty from Frank Lampard in what was a must-win game for both clubs.
There was no way Jose Mourinho's men could afford to lose if they were to remain in with a shout of winning a third successive League title.
This priceless victory reduced Manchester United's lead to six points with both clubs now having nine League fixtures remaining.
City played with a spirit which belied their lowly League placing, although they again lacked fire-power as they failed to find the net for a fourth successive home league match, all of which have ended in defeat.
Indeed, for the most part it was difficult to determine which team was battling for survival and which was challenging for the title.
City's recent misfortune was mirrored by the penalty which handed Chelsea a 28th-minute lead and ultimately was their match-winning goal.
Salomon Kalou cut in from the left and was tripped by City defender Micah Richards enabling Lampard to score from the spot, his 20th goal of another highly productive campaign.
Richards made amends for his error by preventing Chelsea from doubling their lead early in the second half with a fabulous goal-line clearance which saved the day after Lampard had lobbed keeper Andreas Isaksson.
Chelsea brought on former City favourite Shaun Wright-Phillips and within one minute of his entrance he almost sealed victory with a ferocious drive which struck the crossbar.
Then, deep into stoppage-time, Isaksson made a brilliant save to keep out a Michael Ballack free-kick as City remained in with a shout until the final whistle.
Pearce threw on Ishmael Miller, Georgios Samaras and Ousmane Dabo in the final quarter of the game in an effort to conjure an equalising goal which remained elusive.
Though City slipped to another costly defeat at least they won back some respect from the fans who gave them generous applause at the final whistle, instead of the boos and jeers which have become all too familiar in recent weeks.