In a largely uneventful first half, Wimbledon created the first real chance after 11 minutes when Peter Sweeney blasted the ball over from the edge of the box.
Five minutes later, Bradford had their best chance when Kyel Reid fizzed a cross in from the left but, Andy Gray was unable to connect.
Wimbledon's best chance came after 22 minutes when striker Alexander's cross was almost turned into his own net by Bradford's Michael Nelson.
The hosts started the second half brightly, but Toby Ajala wasted a good opportunity having created the chance for himself with a fine solo run from the right.
After 59 minutes, Bradford took the lead, when Alan Bennett failed to deal with a ball over the top from Reid, allowing Garry Thompson through to finish well past the on-rushing Neil Sullivan.
Thompson was in again two minutes later, this time directing his shot just past the post.
The Bradford midfielder was then made to pay for his miss in the 83rd minute as sub Jack Midson headed home following a pinpoint cross from the left from Pim Balkestein.
And things got even worse for the visitors in stoppage time as Ajala's 93rd-minute corner was headed home by Alexander.