After a goalless first half strikes from Mario Balotelli and James Milner - with a thunderbolt - sealed the points for the champions.
Wigan gave City a real battle, mixing it in midfield and causing problems up front and Mancini made a tactical substitution in the second half which led to the Italian being jeered by the travelling fans.
He took off striker Sergio Aguero and put on left-back Aleksandar Kolarov which appeared a negative move, only for the visitors to break the deadlock moments later.
Mancini told Sky Sports: "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.
"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."
Substitute Milner's second settled the game before he limped off and Mancini confirmed that the England midfielder had suffered a hamstring injury, stating: "He was in good form. He's unlucky."
City are now unbeaten in their first 14 games of the season and the Italian expects another tight battle for the Premier League crown with rivals Manchester United.
He added: "It is important that we win. Sometimes it is better to lose one game, maybe, if you then to start to win after you have drawn two or three games in a row.
"The Premier League is difficult to be unbeaten for a year. For us it is important to stay on the top, we are very close to United and I think it will be a fantastic championship."