Trailing Manchester United by 15 points at kick-off, defeat might have led even the most optimistic fan to concede the title race was over, but helped by a great save from Joe Hart of a Frank Lampard penalty the dream lives on.
City spent most of the first half, and indeed much of the match, camped in the Chelsea half thanks to a dominant midfield display but despite many chances they had to wait until the 63rd minute for Toure's sweetly-struck opener into the bottom right.
Substitute Tevez made sure of the three points with a right-footed missile five minutes from time as City put behind them a run of three league games without a win to stand on 56 points from 27 games, seven ahead of third-placed Chelsea.
"I think we deserved to win because we played well, maybe we could have scored more goals," City manager Roberto Mancini, who has faced media speculation over his future this week but who enjoyed hearing his name sung by fans, told a news conference.
Defeat is likely to add further pressure on Chelsea counterpart Rafael Benitez, who by contrast is unpopular among fans, and leaves them more likely to be fighting it out for a top-four finish than the runners-up spot.
In the day's only other Premier League game, Newcastle United beat relegation rivals Southampton 4-2 at home to move six points clear of danger.
On a chilly afternoon on the blue side of Manchester, City were in no doubt as to what would need to be done to keep the title race interesting for a little longer.
Toure shot at Chelsea keeper Petr Cech in the opening minute to set the tone for the first half as the hosts carved out several chances that came to nothing, including three decent opportunities for midfielder Jack Rodwell.
It said a lot about Chelsea that their best first-half effort was a long-range free kick that Lampard sent over the bar.
There was a similar story after the break as City continued to press for an opener, Aguero holding his head in his hands after one miss and lying on the ground in disbelief after fluffing another acrobatic effort.
Instead it was Chelsea, who had forced Hart into his first save moments earlier with an Eden Hazard effort, who suddenly found themselves with a golden chance to take charge when Demba Ba was brought down by Hart and the referee pointed to the spot.
Lampard stepped up, eyeing what would have been his 200th Chelsea goal, but his well-struck 52nd-minute penalty was kept out by the outstretched Hart who had dived to his right.
Benitez acknowledged it had been a tremendous save but questioned why Hart had not been shown a card when it had been a clear goal-scoring opportunity.
"[It should heave been] at least a yellow card," he told a news conference before ruing the missed opportunity to close to within a point of City. "We have to carry on and win our games and fight for the top four."
City's players celebrated Hart's save as if it had been a goal at the other end and found fresh energy for their task.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try your first month for just £1 / $1 / €1
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.