The Argentine's late wonderstrike gave Roberto Mancini's side all three points in a contest they could just have easily lost against an impressive Latics outfit
The home side were frustrated by the well-organised Latics, who created plenty of chances of their own, notably through the impressive attacking triumvirate of Shaun Maloney, Franco Di Santo and Arouna Kone.
City, who lost Sergio Aguero to injury at half-time, stepped it up after the break but could not find an elusive opening goal, with replacement Edin Dzeko missing a great chance before Tevez's moment of magic secured a gutsy win.
Wigan started brightly but the hosts mustered the first real opening, Aleksandar Kolarov flashing a free kick just inches wide of Joel Robles's left-hand post as the Spaniard stood motionless.
City began to monopolise the ball more and more and were pressing very high on the Wigan defence, who were hassled and harried into numerous mistakes.
Aguero, who almost latched onto a ball over the top from Yaya Toure just moments before, looked the likeliest to break the deadlock and nearly did so after tricking his way down the byeline before curling just wide of the far post.
Kolarov, on the other hand, was particularly wasteful with his final ball from the left as he squandered a brilliant opportunity to play in Samir Nasri after Tevez had threaded a ball through to him.
As the half wore on, though, the more frustrated City became with a Wigan side who were not only dealing with the hosts' plethora of attacking riches but also causing problems for the City defence, with Kolarov frequently targeted.
The ploy nearly paid off as Wigan wasted the first half's best chance. A lovely move involving Kone, who tricked his way brilliantly past Vincent Kompany, and Maloney resulted in Di Santo sidestepping his way past the woeful Kolarov and Joleon Lescott but the Argentine's side-footed effort was superbly kept out by the sprawling Joe Hart.
Moments later City almost produced an immediate sucker-punch of their own as Tevez raced away down the right and sent in an inviting centre with which Aguero somehow failed to connect from just a few yards out.
Wigan began the second period just how they ended the first, frustrating a City side bereft of ideas in midfield and came close to grabbing the all-important opener twice in the opening exchanges.
First, the instrumental Maloney curled a sublime effort beyond Hart but found the towering presence of Lescott on the line, who lashed clear.
Then, after more intricate Latics play, Di Santo played in the unmarked Kone but his first touch let him down and Kompany recovered to clear as the home side were made to weather a storm.
Their hard work was almost undone when substitute James Milner's low cross eluded everyone in the area, with fellow sub Dzeko and Nasri unable to apply a telling touch.
The game became an end-to-end affair, with Wigan sub Callum McManaman coming close with a low shot before Dzeko missed an even more presentable chance, firing straight at Robles when clean through.
Just when it appeared as if City had run out of ideas, up stepped Tevez to produce the moment of quality for which the game had been crying out, as he skipped his way past a couple of challenges before bending a sumptuous strike beyond the despairing Robles to send the Etihad Stadium into raptures and give City a flicker of hope in the title race.