Not since they were relegated from the Championship at the end of the 2003-04 season have Bradford reached the third-round stage, while the victory avenged a 2-1 home defeat in the league at the end of September.
Bradford went in front after nine minutes when Craig Fagan’s right-wing cross was headed down by James Hanson for fellow striker Ross Hannah to flick the ball over the head of goalkeeper Seb Brown.
The home side increased their lead five minutes later when on-loan midfield player Ricky Ravenhill’s cross was turned into his own net by defender Chris Bush.
Wimbledon pulled a goal back five minutes after half-time when Jack Midson took a pass from Ricky Wellard and scored with a low, 10-yard shot just inside the far post.
But Bradford restored their two-goal advantage in the 70th-minute when substitute striker Nahki Wells was brought down by visiting skipper Jamie Stuart and Fagan scored from the penalty spot.