City still in the hunt as Tevez sinks Villa
Tevez punished Ciaran Clark's calamitous mistake in first-half added time at Villa Park to enable second-placed City to move within 12 points of runaway leaders Manchester United.
It was far from a vintage performance from Roberto Mancini's team, but the victory at least preserved their faint hopes of catching bitter rivals United.
Villa, meanwhile, remain in 18th and were once again left to rue a costly lapse of concentration from one of their players at a key moment.
Their forthcoming matches against fellow strugglers Reading and QPR now take on even further importance as Paul Lambert's team try to beat the drop.
Villa created their best chance of the first half after 21 minutes when it required a Tevez clearance off the line to keep out Christian Benteke's header from Charles N'Zogbia's corner.
It was a narrow escape for the visitors and they responded almost immediately by registering their first genuine attempt of the game when Jack Rodwell's vicious shot had to be palmed over his crossbar by Brad Guzan.
It was to be Rodwell's final meaningful contribution after he limped off shortly afterwards to be replaced by Edin Dzeko.
City threatened in the 32nd minute when a free-kick from James Milner, up against the club he left to join City, evaded the wall, however Guzan was equal to it.
Villa had a fortuitous escape eight minutes before the interval when Yaya Toure and David Silva combined for feeding the onrushing Pablo Zabaleta, yet the captain's arcing shot ricocheted against the inside of the left post before being hooked to safety.
Guzan had to be at his best to thwart the dangerous Tevez, clawing away a curler which looked destined for the top-right corner.
As the clock ticked down in added time, Villa appeared to have survived the onslaught, but then came Clark's moment to forget.
The defender, Villa's last man, received a throw-in but loitered in possession. With Dzeko now upon him, he elected for a drag-back in a desperate attempt to get himself out of trouble only to slip.
Dzeko charged through before squaring to Tevez who, in typically clinical fashion, sold Guzan with a dummy before slotting past the beleaguered Clark, by now desperately attempting to make amends on the line.
It was ruthless finishing and, although harsh on Villa, they only had themselves to blame - Clark's furious protests for a foul by Dzeko were waved away by referee Mike Dean.
City picked up where they left off in the second half and Dzeko almost increased their lead with a half volley which bounced agonisingly beyond the left post.
Matthew Lowton denied City a certain second in the 55th minute with a clearance off the line to deny Tevez after another weaving run from the Argentina international.
At 1-0, Villa always stood a chance and they continued to battle manfully with a Gabriel Agbonlahor header and crisp Lowton drive both flashing wide.
Yet as they pressed forward for an equaliser, the openings increased for City at the opposite end and Guzan excelled once more with a fingertip stop to push Yaya Toure's low shot against the post before Dzeko's follow-up was ruled out for an offside.
Villa's frustration was compounded in the final moments when Fabian Delph picked up his 10th booking of the season, meaning he will miss their next two matches.