The Sky Blues came away from the scrappy affair with all three points after some tactical tinkering from the Italian.
He brought off star striker Sergio Aguero for full-back Aleksandar Kolarov in what initially appeared to be a defensive move.
However, City went on to take the lead and eventually the win.
Mancini explained his reasoning for his decision after the game and praised his team for grinding out a positive result:
“Wigan play with three defenders and two in the channels. I wanted to put players in the same positions as them and when we changed it, we scored the first goal. After that, the match changed.” He told SkySports.
“I am happy. We didn’t play very well in the first half, we know Wigan are a good team. They play good football. We knew this before the game.
“When we have played against Wigan it has been a difficult match because they play very well.”
Mario Balotelli gave the champions the lead after showing persistence in the Wigan area, before James Milner smashed home a second late on.