In a tactical battle with defences largely on top throughout, Tevez's moment of inspiration just before the hour proved to be decisive.
Chelsea were unable to halt the South American's burst from halfway and he found the perfect finish too, through Ashley Cole's legs and in off the post.
Carlo Ancelotti's men battled hard to force an equaliser, but, just as they had done for most of the contest, they failed to open up a disciplined City defence and came no nearer than the header Branislav Ivanovic struck the bar with before half-time.
It rather showed up the opinion Roberto Mancini offered yesterday that Chelsea would win the title easily, and signalled City can join Manchester United and Arsenal in harbouring genuine hopes of glory next May as well.
It was slightly strange that the build up to a game between the Premier League's biggest spenders should be centred around respective injury problems.
Yet that is exactly how it turned out, Ancelotti claiming he had just 12 fit players, which was one more than Mancini.
Defensively, City are struggling with neither Joleon Lescott nor Jerome Boateng - who did make his debut as a late substitute - considered fit enough to start.
And once Wayne Bridge had failed a pre-match fitness test on a thigh injury it was anticipated would keep him out for another fortnight anyway, Mancini went for 19-year-old Belgian Dedryck Boyata, normally a centre-half, to make only his fourth league appearance.
Boyata rewarded his manager with a solid contribution to an obdurate defensive performance from City.
Only once were the Blues opened up properly, and that had nothing to do with the teenager.
In fact it was Tevez who drifted away from Florent Malouda as he anticipated a return pass to Didier Drogba, who had just taken a corner on the Chelsea left.
Tevez's movement gave Malouda the space to curl a deep cross to the far post, where Alex nodded it back to Ivanovic.
The Serbian had two goes at putting Chelsea in front. The first came bouncing back off the bar, giving him a second header to go for, this time Joe Hart making a comfortable save.
Apart from that, both goalmouths were largely underused.
Knowing this was their biggest test of the season so far and without Frank Lampard to drive them forward from midfield, Chelsea were content to play within themselves, keep a fairly rigid shape and let City expend their energy trying to break them down.
For their part, the home side failed to get sufficient support to Tevez, who worked incredibly hard up front on his own but was limited to speculative long-range efforts.
Under such circumstances, it was hardly a surprise it began to get a bit tetchy and Pablo Zabaleta's booking for a reckless sliding tackle on Ivanovic gave way to a period of play scarred by physical confrontation.
The first two minutes of the second period produced as much intense action as there had been in the whole of the first.
After Hart had pushed a curling Nicolas Anelka shot away from danger, Michael Essien should have done far better with the near-post corner than send his header sailing over the bar after being picked out completely unmarked.
City responded with their first meaningful assault on the Chelsea goal, which forced Cech to make a decent low save to deny Silva.
It proved to be the prelude to the deadlock being broken.
Yaya Toure and the nippy Silva deserve mentions for their short pass and running off the ball respectively after Ramires had conceded possession just inside the City half.
The rest of it was all the South American's own work as he ran ferociously at the visitors' defence, jinked to his right, then blasted a shot through Cole's legs and into the net off the inside of Cech's right-hand post.
Twice Essien tried to level from long-range. Twice his radar was way off and the ball sailed over.
Alex glanced a header wide after Boyata had marred his effective performance by getting booked for chopping down Yuri Zhrikov, but with Cole also belting a shot into the side-netting, Chelsea ran out of ideas.
After beating the Chelsea twice last season as well, City are rather getting to like this.