Man City couldn't find a way past Wigan until the 16th-place team was reduced to 10 men in the 56th minute when Gary Caldwell was sent off for a foul on Tevez on Monday.
"At halftime, the boss (Roberto Mancini) wasn't happy and he let us know about it," City goalkeeper Shay Given said. "We just didn't have enough tempo in our game and we weren't getting in and about Wigan. But we turned it around and Carlos Tevez was outstanding for us."
Tevez broke the deadlock in the 72nd by tapping into an empty net after goalkeeper Vladimir Stojkovic missed Patrick Vieira's high ball due to a mix-up with teammate Paul Scharner.
The Argentina striker added another two minutes later after Vincent Kompany had flicked on a cross from Adam Johnson.
Tevez glided into the penalty area before side-footing into the net in the 84th to claim his 25th goal since joining City in the offseason.
"After the sending off, it was too easy - the red card changed the game," Mancini said. "Carlos is a fantastic striker and I hope he continues like this in the run-in. If we fight like we did in the second half, we will probably finish fourth."
Liverpool had beaten Sunderland 3-0 on Sunday to move to fifth but City reclaimed the position and is two points behind fourth-place Tottenham.
Wigan is four points above the drop zone with six matches left. Newcastle is set to make an instant return to the Premier League after beating Nottingham Forest 2-0 on Monday to lead the League Championship by four points over West Bromwich Albion.