Imperious in recent weeks, City were looking to reclaim top spot from Arsenal and move six points above Chelsea, but it was the visitors who prevailed thanks to a 32nd-minute bullet by Branislav Ivanovic.
City had won all 11 of their previous home league games this season, losing only to European champions Bayern Munich on home turf, while it was the first time they had failed to score at the Etihad in the league since November 2010.
The hosts had been seeking a ninth successive league win, but instead Jose Mourinho's Chelsea were left to celebrate a home-and-away double, having beaten City 2-1 at Stamford Bridge in October's reverse fixture.
Chelsea also hit the woodwork on three occasions, but Ivanovic's vicious strike proved enough as they moved level on points with City, two points shy of leaders Arsenal.
City were without top scorer Sergio Aguero due to injury, while Martin Demichelis had to fill in for the injured Fernandinho in central midfield, but the hosts attacked with their usual abandon nonetheless.
Aleksandar Kolarov whipped a cross across goal that narrowly eluded Yaya Toure, who then clipped a shot just over from the edge of the box before striding to the byline and teeing up David Silva to sweep an effort narrowly wide.
Edin Dzeko curled off-target after giving David Luiz the slip, but City's gung-ho advances left them exposed at the back and Joe Hart had to save from Ramires in the 27th minute after a cut-throat Chelsea counter.
It was a reminder of the visitors' pace on the break and five minutes later another raid saw them go ahead.
Branislav breaks through
Vincent Kompany did well to block from Ramires, who had been picked out by Eden Hazard, but as the ball rolled to the edge of the box Ivanovic met it with a devastating left-foot drive that flew into the bottom-left corner.
With City rattled, the irrepressible Hazard worked Hart with a low strike before skipping past Pablo Zabaleta and crossing for Samuel Eto'o, who could only slam against the crossbar from a narrow angle.
An exchange of chances saw both sides go close early in the second half, with Toure drilling a shot a whisker wide at one end before Nemanja Matic clipped the post with a 30-yard thunderbolt at the other.
City manager Manuel Pellegrini sent on Stevan Jovetic for Negredo in the 56th minute, but Chelsea continued to threaten, with Cahill heading against the post from an in-swinging Willian corner.
The hosts responded, Dzeko miscueing from a Zabaleta centre, while Silva drew a fine one-handed save from Cech with a dipping free-kick before clattering the ball wide from a Kolarov cross.
Forced deeper and deeper as the game wore on, Chelsea were incensed when City defender Matija Nastasic was only shown a yellow card for a last-man foul on substitute Oscar on the halfway line.
Jovetic then forced Cech into another eye-catching save with a shot from range in injury time, but Chelsea were to have the last laugh.