City looked on course for a draw at Stamford Bridge after a Sergio Aguero thunderbolt cancelled out Andre Schurrle’s opener, only for Torres to pounce at the death after a mix-up between Matija Nastasic and Joe Hart.
It was the latest in a series of blunders by England goalkeeper Hart, who rushed to the edge of his area but did not clam the ball, and he could be seen venting his frustration as Torres wheeled away to celebrate.
Jose Mourinho’s Chelsea have now won five consecutive games in all competitions and trail leaders Arsenal by just two points.
“We won a game which was very important for us. We beat maybe the best team in the Premier League,” said Mourinho, who reacted to Torres’s winner by leaping into the crowd.
“Everything happened for Torres after he missed an easy chance. After that, we saw the best Fernando.”
City manager Manuel Pellegrini, who was succeeded by Mourinho at Real Madrid, saw his side finish the weekend down in seventh place, four points below Chelsea and six shy of Arsenal.
“In the second half we were in control of the ball, but what happened is what has happened to us in other away defeats,” Pellegrini said.
“I don’t know if this is the moment to say who has to take the ball (for Torres’s goal). They scored a goal and we will analyse it in the week.”
In the continued absence of injured City captain Vincent Kompany, Martin Demichelis was handed his debut at centre-back, while Aguero was deployed as a lone striker in a cautious 4-2-3-1 system.
Chelsea recalled Ashley Cole at left-back, in the only change to the team that won 3-0 at Schalke in the Champions League in mid-week.
Mourinho wore a broad smile as he settled into the dug-out and his side started positively, with Gary Cahill volleying over from a deep Oscar cross and Torres heading straight at Hart.
City’s extra man in midfield enabled them to establish a foothold in the game, however, and they saw Samir Nasri drill narrowly wide before Aguero poked a shot at Petr Cech after wriggling between a pair of defenders.
It was attritional fare, but in the 29th minute Torres found himself with only Hart to beat from Ramires’s pass, only to hook an ugly half-volley high over the bar from just 10 yards out. But he was quick to atone.
In the 33th minute, he outpaced Clichy with a burst of acceleration down the right flank and then squared the ball for Schurrle to steer in his first Chelsea goal from close range.
Encouraged, Torres almost extended the hosts’ lead four minutes later, but after slipping away from Demichelis, he saw his right-foot curler come back off the angle of post and bar.
Aguero stung Cech’s gloves shortly before the interval, while Yaya Toure headed over, but although Chelsea reached half-time with their lead intact, it took the visitors only four minutes to equalise after the break.
Aguero seemed to pose only a marginal threat as he scampered in behind the Chelsea defence to collect Nasri’s pass, but he surprised Cech with a ferocious first-time shot that fizzed into the top-left corner.
It was his fifth goal in three games, and Cech did not even see it.
There were chances for both sides from set-pieces — Garcia heading straight at Cech, Hart saving from Torres and John Terry volleying over — before Cech had to use his feet to thwart David Silva.
Aguero came close to claiming a second with a delicate chip that floated just wide, but instead it was Torres who struck the decisive blow thanks to a calamitous defensive blunder.
Hart came out to field Willian’s aimless pass, only for centre-back Nastasic to head the ball past him, and Torres outpaced Demichelis to stab home and send Mourinho springing jubilantly from the bench.