The 48-year-old's tactical change in the second period paid instant dividends as the champions ruthlessly put two past an impressive Latics side at the DW Stadium
Efforts from Mario Balotelli and James Milner sealed all three points for the visitors against the Latics, who had been the better side for most of the match.
The goals came after Mancini altered his formation from a flat back four to three, in order to match up against Wigan, a ploy which paid instant rewards.
"They play with three defenders, two in the channel so I wanted to put players in the same position," Mancini told Sky Sports.
"We changed [formation] but we were lucky because we scored the first goal and the match changed."
Despite a poor first half showing, the Manchester City boss was always confident his side could turn it around in the second period.
"Every year when we play against Wigan its difficult because they play very well," he continued.
"After the first half I thought we have another 45 minutes and three or four players on the bench that can change the game."
The win means City continue their unbeaten record in the Premier League, which now stands at 20 games, but Mancini says he is more concerned with keeping pace alongside Manchester United at the top of the table.
He added: "Maybe it's important that we win because it's sometimes better to lose one game than draw two or three in a row. The Premier League is difficult to be unbeaten, so for us it's important to stay at the top and stay close to [Manchester] United."