Following their midweek Carling Cup exit at Blackburn Rovers, Chelsea saw their lead at the top of the Premier League cut to a slender two points as City reinforced their own bid for a top-four Champions League spot.
After a club-record run of seven successive league draws, City finally rediscovered their winning touch to record their first win in the league since late September.
And after an impressive display, City fans must be wondering how they failed to beat Fulham, Burnley and Hull in their last three home league fixtures.
City, who were without the injured Craig Bellamy and Stephen Ireland, received a let off moments before Chelsea took an eighth minute lead when keeper Shay Given denied Didier Drogba with a fine save.
The warning was not heeded as Chelsea went ahead with a goal which bordered on farce as Given pulled off super stops to foil Branislav Ivanovic and Nicolas Anelka, only for the second to cruelly ricochet off the back of Emmanuel Adebayor and into the net from a couple of yards.
City began to exert considerable pressure on the Chelsea goal and were unlucky when a header from Micah Richards was spectacularly cleared off the line by Ricardo Carvalho.
They were finally rewarded with a 37th minute leveller as they breached the Premier League's meanest defence.
And it was Adebayor who found the net at the right end with a close-range shot after a drive from Shaun Wright-Phillips deflected off Micah Richards and into his path.
City continued where they left off after the restart when Ivanovic made a goalline block to thwart the ever dangerous Adebayor, but it was not long before they took a 56th minute lead.
Carvalho was penalised for a foul on Wright-Phillips on the edge of the penalty area and Carlos Tevez bent the free-kick round the defensive wall and low to the left of keeper Petr Cech, who was initially wrong-footed by the delivery.
Chelsea were given the chance to draw level in the 82nd minute when substitute Nedum Onuoha tripped Drogba in the box, but Frank Lampard's spot kick was brilliantly saved by Given diving low to his left.
City received another escape late on when Michael Essien released Drogba who burst through on goal only to fire narrowly wide when pressurised by Joleon Lescott.