The Argentina striker came to City's rescue after they had toiled for more than 70 minutes to make a breakthrough against spirited Wigan before he increased his goal tally for the season to 25.
And it was only when Wigan were reduced to 10 men after Gary Caldwell's sending off early in the second half that City eventually took control following an ineffective display until that point.
Manager Roberto Mancini had rung the changes following the home defeat by Everton in their last match as Craig Bellamy, Gareth Barry and Micah Richards dropped down to the bench, while Stephen Ireland was ruled out through injury.
City experienced a largely frustrating opening half in which they only created two genuine chances which both fell to Tevez.
The in-form striker was first foiled by a splendid save from keeper Vladimir Stojkovic, who was deputising for the unwell Chris Kirkland, and he then curled a delightful shot agonisingly wide.
Wigan more than matched City in the opening period in which keeper Shay Given also had to pull off two super saves to thwart Hugo Rodallega and Paul Scharner as the visitors threatened to dent their opponent's push for a Champions League place.
The turning point in the match came in the 56th minute when Wigan were reduced to 10 men after central defender Caldwell was harshly sent off for a sliding challenge on Tevez.
Yet City struggled to make their extra man count until Tevez finally made a breakthrough in the 72nd minute with a highly controversial goal as Wigan claimed Emmanuel Adebayor ought to have been penalised for a raised-foot challenge on Stojkovic after the keeper failed to gather a Patrick Vieira through ball, leaving Tevez free to walk the ball into the empty net.
Three minutes later and Tevez struck again lurking at the far post to convert a low left-wing cross from Javier Garrido following a short corner by substitute Bellamy.
Tevez completed his hat-trick in the 84th minute with a sublime finish was he cut in from the right and steered a well-placed shot into the far corner to send home the City fans in a joyous mood after they had become increasingly frustrated the longer the game had remained goalless.