Neither side managed a shot on goal in the first-half. Dons midfielder Darren Potter, playing against his old club, had perhaps the only meaningful effort when he fired over from just outside the area.
Wednesday goalkeeper Richard O'Donnell was called into action for the first time early in the second-half, saving Jabo Ibehre's low shot.
Madine opened the scoring after 54 minutes with his side's first shot on target after Clinton Morrison found him unmarked in the area. He found the net again in the 63rd minute, powering a header past David Martin after getting on the end of Liam Palmer's right-wing cross.
Substitute Angelo Balanta pulled a goal back for the Dons with a superb individual effort, evading several challenges before beating O'Donnell with a firm drive. Dean Bowditch went close to equalising moments later when his long-range effort forced O'Donnell to make a fine save to his right.
Palmer completed the scoring a minute from time after trading passes with Madine before Ibehre was sent-off following a second booking in stoppage time.