Latics were trailing until the 89th minute when substitutes Josh McEachran and Marc-Antoine Fortune combined to devastating effect.
McEachran, making his debut after joining on loan from Chelsea, dissected the defence with a delightful through ball that was expertly finished by Fortune.
And then fellow substitute Jordi Gomez won it for Wigan on the stroke of full-time with a marvellous free-kick from 25 yards.
Rosler said: "I remember not so long ago at Brentford, against Colchester, I took off Adam Forshaw - probably our best player - and the crowd was chanting 'you don't know what you're doing'.
"I brought three players on - two of them scored and the other made a goal. Sometimes you need a bit of luck and we got that with the substitutions."
Rosler also felt his side deserved their break for continuing to play football and not resorting to 'route one' in search of a lifeline.
"I didn't want to go long," the German added. "The temptation is to do that, and we don't have the players to do that.
"For me, the only way we were going to come back into the game was by playing football, and that's the reason I made the changes I did."
- Sports & Recreation
- American Football
- Josh McEachran
- Adam Forshaw
- Jordi Gomez