The game was a scrappy affair, but despite edging the contest as a whole, City switched off twice late on and it cost them dear.
Garry Thompson's emphatically taken volley following a defensive error put The Bantams ahead just before the hour; but late goals from Jack Midson and Gary Alexander handed AFC Wimbledon a first home victory in the league since late October.
The game began in scrappy fashion and following a bout of head tennis in and around the Bradford penalty area the ball fell to Rashid Yussuff and his deflected effort was comfortably saved by Matt Duke.
City's first attempt of note came from Kyel Reid. His on flick on was knocked down by Garry Thompson and he hit a vicious dipping shot from 20 has that dropped narrowly over the bar.
The Dons then came inches away from opening the scoring; Harry Pell's cross almost fell to Toby Ajala but instead came out to Peter Sweeney and the former Leeds midfielder's sweet first time shot fizzed narrowly over the bar.
Gary Alexander was found in dangerous amounts of space inside the area and his low cross was almost turned in by Yussuff but Matt Duke held the ball well.
Garry Thompson was leading the line well like he did at Wycombe 4 days earlier and his knock down allowed Will Atkinson to hit a rising half volley a yard or so over the bar from the best part of 30 yards.
Will Atkinson was given an identical opportunity to his last when Andy Gray knocked down a long ball into his path but he could only manage to fire his shot harmlessly over the bar.
The Bantams started the second half brightly and Kyel Reid showed attacking flair to burst away from 2 blue shirts and into space in front of him, his resulting shot, however, flew harmlessly over the bar.
Toby Ajala was looking dangerous for the hosts and he forced Duke into a save with a low shot through a crowd of players when Peter Sweeney's freekick was half cleared only as far as him.
City took the lead shortly before the hour mark; a long ball forward was flicked on and AFC Wimbledon skipper Mat Mitchel-King attempted to guide the ball back to Neil Sullivan with a header, Garry Thompson read his decision and latched onto the loose ball to fire a superb volley into the top corner from inside the area.
A minute later Garry Thompson was sent chasing a loose ball to bear down on goal, he had the pace to evade the last man but he scuffed his shot wide of the target and the chance of a second goal in as many minutes had gone.
Another defensive mix up from the hosts allowed Kyel Reid to scamper forward with intent. His resulting low drive crept narrowly wide of the far past with Sullivan a spectator.
City were really taking the game by the scruff of the neck and looked far more likely to score next than their hosts. Stephen Darby's hanging cross was met by the head of an inspired Garry Thompson but his effort went a couple of yards wide.
Against the run of play, Wimbledon equalised. A hopeful cross into the area was met by substitute Jack Midson whose header bounced beyond the reach of Matt Duke and nestled into the bottom corner.
Deep into injury time, The Bantams switched off once more and it ultimately cost them a share of the spoils. Toby Ajala's first corner was fizzed into the near post and put behind for another corner. Ajala's second delivery was identical to the first but it was capitalised on by a determined Gary Alexander who stole in unmarked to power the ball beyond Duke.
City had seemingly done enough to win, but whilst the margin remained at one goal, Wimbledon were very much still in the game and two defensive lapses cost them dear in their final game before Sunday's Wembley showdown with Premier League Swansea City.