The Argentine's 11th goal of the season saw City narrow the gap on rivals Manchester United to 12 points - but Roberto Mancini's side suffered another injury blow to Jack Rodwell.
Carlos Tevez keeps Manchester City's title defence hopes alive with winner against Aston Villa
Roberto Mancini admits his relief at watching Manchester City keeping their slim hopes of retaining the English Premier League title alive with a narrow victory over Aston Villa has been tempered by another injury setback to Jack Rodwell.
But midfielder Rodwell, signed from Everton during the summer, suffered a recurrence of his hamstring injury midway through the opening period and will be sidelined for "three to four weeks".
Mancini said: "We are very sorry for Jack, because he is a good guy, a good player, but he is unlucky. It is his hamstring.
"I think it is impossible to resolve his problem after six or seven months because he's had this problem for five or six years and we need maybe more time.
"How long will he be out? Maybe he will be back after the international break, three or four weeks. It is the same injury.
"I am very sorry because he is a young player. He needs to improve but he has played very well against Chelsea and was playing very well tonight."
Tevez, in the side as a replacement for injury victim Sergio Aguero, was a constant threat to the Villa backline, who needed several fine saves from goalkeeper Brad Guzan to keep them in the match.
Paul Lambert's side had started brightly against the visitors, however, with Joe Hart unconvincing while trying to punch clear a Joe Bennett cross, and Matija Nastasic kept under pressure by Christian Benteke.
City were relieved when a dipping centre across the face of goal from Bennett just eluded the lunge of Andreas Weimann, and Tevez was forced to scramble a Benteke header off the line halfway through the first period.
But once the champions asserted control it was one-way traffic, until finally Tevez broke the deadline in injury-time with his 11th goal of the season.
Ciaran Clark was caught in possession by City substitute Edin Dzeko, and appealed in vain for a foul as the forward threaded the ball through to Tevez, who kept calm and cut back inside the box before slotting past Guzan on the edge of stoppage time.
The second half saw City continue to put pressure on Villa, but failed to build on their lead. Yaya Toure came closest, his low shot hitting the post, but Dzeko had strayed offside before converting the rebound.
Afterwards Mancini repeated his determination that City will not give up on the title without a fight but admits they probably have to win their 10 remaining games.
He said: "It is difficult because we have 30 points to play for and we need to try to win.
"At the end, we will see what happens. In football everything can happen right up to the last second.
"We probably need to win all 10 matches that are left. We need to win all the matches.
"If they lose three or four or five games.....it is difficult because they are too strong for this.
"When you have to win always, it is difficult to win every game. But last year we did this. Why can't we do it this year?"
The result leaves Villa remain in the bottom three, with Lambert admitting Clark's mistake was the crucial moment.
"I thought we were well in the game," he said.
"The goal is a mistake. I wouldn't have minded if someone had put one in the top corner with a bit of skill.
"But it's a mistake by us. It is easy to be critical of Ciaran. The lad has been excellent all season. He will learn from it, he won't make the same mistake again."
The Villa boss knows the significance of the next two matches.
He said: "The next two games are massive for us. If we play like that, we will give teams a fright, that's for sure."
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