Despite that setback, Wigan were still very much in the game and Fraser Fyvie forced Martin into a good stop with a powerful shot. Martin was then involved again, tipping the ball away from McClean at the back post.
The away side continued to have the better of the play, but Roger Espinoza fired narrowly over the bar when well placed.
The Latics then worked the ball to the edge of the area early in the second half, before Fyvie drilled a low shot wide of the left post.
Marc-Antoine Fortune battled his way down the flank and crossed the ball to the middle for McClean, but he got it stuck under his feet and MK Dons were able to clear.
Despite showing enough quality in attack, Wigan needed Al-Habsi to keep it at 1-0 when he tipped over Dean Bowditch's header. However, they eventually equalised through Nick Powell's close-range shot.
Neither side could find a winner in normal time, but with extra time just two minutes old, Powell surged through the home defence and clipped his shot over the goalkeeper.
Jordi Gomez scuffed a right-footed shot wide when through on goal, but Wigan settled the match when Fortune's low shot found the back of the net.
The Cup holders now face Crystal Palace at home in the next round.