Gary Cahill and Fernando Torres had spurned golden opportunities before the latter laid on Andre Schurrle to score his first Chelsea goal and give Jose Mourinho’s men a deserved half-time lead.
Sergio Aguero’s thunderous strike – his sixth goal in four outings and 10th of the season – left Petr Cech grasping at thin air three minutes after the restart, and the equaliser prompted a sustained spell of City pressure.
Manuel Pellegrini's team appeared the most likely winners heading into the closing stages, but as they pressed, Chelsea substitute Willian launched a hopeful ball forward and City defender Matija Nastasic headed back towards his own goal, only to see the on-rushing Hart miss the ball to leave Torres with a simple finish for the winner.
Ashley Cole returned to displace Cesar Azpilicueta in Mourinho's only change to the Chelsea XI that beat Schalke 3-0 in the UEFA Champions League.
Vincent Kompany’s continued injury absence with a thigh complaint meant that City boss Pellegrini handed Martin Demichelis a debut at centre-back and pushed Javi Garcia into a holding role to match Chelsea's three-man central midfield.
The reshaped heart of the visitors’ defence was found wanting in the third minute as a corner was partially cleared and Oscar found Gary Cahill, who blazed over when unmarked at the back post.
City proceeded to dominate possession in the first quarter of the match without fashioning a clear chance and they offered up another for the hosts in the 29th minute.
For a second time, their backline was virtually non-existent as Torres ghosted onto Ramires' pass, only to fire over with the goal at his mercy.
The striker atoned for his error three minutes later, though, with an electric burst of pace to beat Gael Clichy and cross for Schurrle to enjoy a simple finish.
A seemingly rejuvenated Torres subsequently tormented City's other full-back, Pablo Zabaleta - cutting in past the Argentina international and his countryman Demichelis to rattle Joe Hart's crossbar with a superb curling effort.
Petr Cech then beat away a rasping shot on the turn from Aguero in the 42nd minute as City pressed for a way back into the game.
But Cech could do nothing four minutes after the break when the in-form striker made light of an acute angle to drill Samir Nasri's throughball into the top corner.
Chelsea were suddenly reeling and Cech gratefully grasped Garcia's free header from David Silva's free-kick after Ramires had become the fourth player into referee Howard Webb's notebook for hauling down Nasri.
From similar situations at the other end, Torres and John Terry passed up opportunities from Frank Lampard deliveries and, by the time Cech's left boot had denied Silva in the 65th minute, the contest was wide open.
Aguero searched for another inspired intervention as he lobbed over the far corner following a lightning-quick break involving Silva and substitute Jesus Navas, but it was Torres - and the unfortunate Hart - who were to have the final say.
