The Yorkshire club now progress into the quarter finals of the Capital One Cup following their determined victory.
Manager Phil Parkinson said: "I am ecstatic. I thought it was a night of great discipline by the team. There were a lot of big hearts out there.
"Wigan give you problems that are ones we don't normally come up against in League Two, in terms of the movement of the team and their shape.
"In the first 15 minutes we found it tough to cope with, but as the game went on, the discipline and commitment of the team grew. I am really proud of the team tonight.
"Everyone stuck to the job over the 120 minutes and we got our rewards for that.
"If you play with commitment, desire and discipline like we did tonight you do get rewarded and I am really pleased with the way we played."