Torres had earlier set up Andre Schurrle brilliantly to make it 1-0 to the Blues after 33 minutes, only for Sergio Aguero to power in a superb leveller in the 49th minute.
Both sides had chances in an exciting finale but it looked like they would have to settle for a point apiece until Torres capitalised on a defensive mix-up between Matija Nastasic and Joe Hart to seal victory.
Jose Mourinho kept faith with Torres up front following his two goals against Schalke and Chelsea began brightly as they looked to test a defence marshalled by Nastasic and debutant Martin Demichelis in the absence of injured captain Vincent Kompany.
However, after one anxious moment when Gary Cahill volleyed over the top as the offside flag stayed down from an Oscar cross, Manuel Pellegrini's side soon settled and began to enjoy the majority of possession.
The decision to leave Alvaro Negredo out of the starting line-up did at least give City an extra man in midfield and allow Yaya Toure greater freedom to push forward, with Aguero threatening on one run before scuffing a shot at Petr Cech from a tight angle.
There was a flurry of yellow cards before the first clear chance of the afternoon arrived on the half-hour mark when Ramires' clever pass left Torres one-on-one with Hart, but the Spaniard fired horribly high of the goal.
Torres' fragile confidence has been the subject of scrutiny for several years but he shrugged off the bad miss to create Chelsea's opening goal with an excellent run three minutes later, as he showed great pace to burst past Gael Clichy and deliver a low cross from the byline which presented Schurrle with the simplest of close-range finishes.
Torres continued to cause havoc and he nearly doubled Chelsea's lead with a powerful strike from the corner of the penalty box which smashed against the crossbar.
Cech was called into action to deny Aguero from a narrow angle before the interval but he was unable to prevent the Argentina international from equalising in sensational style four minutes into the second half.
Aguero raced on to a pass from Samir Nasri and unleashed an unstoppable early shot with his left foot which Cech was slow to react to as it flew into the top corner of his near post from the edge of the area.
Chelsea had to withstand a short period of intense pressure as City went in search of a second goal, but Javi Garcia could only head straight at Cech from David Silva's free-kick after Nasri had been sent tumbling by Ramires just outside the box.
The home fans responded to drive their team back on to the front foot and there were strong appeals for a penalty when Eden Hazard went down in the area under a challenge from Pablo Zabaleta, but referee Howard Webb waved play on.
There was no sign of either side settling for a point as the game remained open, with Silva forcing Cech to make a save with his legs at one end and Oscar blazing a free-kick high into the stands at the other.
While Torres had looked the main danger in the first half, it was Aguero who appeared most likely to grab the headlines as the game wore on and he lifted a delightful chip just wide of the post after Webb had played an advantage.
Ramires drove a long-range effort off target and substitute Willian's free-kick just evaded a diving Branislav Ivanovic as it drifted wide of the far post, while Samuel Eto'o was sent on to partner Torres as Chelsea tried to finish with a flourish.
And Chelsea were rewarded in the 90th minute when Torres chased a hopeful long ball from Willian and a communication breakdown at the back for City resulted in Hart charging to the edge of his box and Nastasic heading it beyond his goalkeeper, giving Torres the chance to turn in the winning goal.