City, five points behind fourth-placed Tottenham Hotspur before kickoff, struggled until Wigan's Gary Caldwell was shown a red card for a foul on Tevez after 56 minutes but finally clicked into gear thanks to the Argentine striker.
Roberto Mancini's side moved to 56 points from 31 matches, two more than Liverpool who have played 32. Tottenham, who City still have to play at home, have 58 points from 31.
After spending vast sums of owner Mansour bin Zayed Al Nahyan's money on signing the likes of Tevez, Emmanuel Adebayor and Roque Santa Cruz, fourth spot and a chance of Champions League football was the minimum requirement for City.
Tevez brought that possibility a step closer at Eastlands with an inspired second-half display which brought him three goals in 13 minutes.
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Wigan, desperately trying to stay clear of the relegation zone, still looked dangerous after Caldwell's slightly harsh sending-off but Tevez put City ahead on minutes when he tapped in as Wigan keeper Vladimir Stojkovic failed to gather a routine ball under pressure from Adebayor.
Another simple finish made it 2-0 two minutes later and Tevez wrapped up the points with his best effort of the night, a classy finish after waltzing into the Wigan area.
