Delroy Facey, who has joined the club on loan from Bolton Wanderers soon made his mark with a goal after only seven minutes.
Michael Standing ran down the right and swung a low cross towards the near post. Facey then flicked the ball across keeper Kelvin Davis from a tight angle to find the bottom left corner.
Moments later the Dons should have levelled. A corner was whipped across the face of the City goal. Neil Shipperley managed to get his foot to the ball but he stabbed it past the post from close range.
City suffered a big blow on 23 minutes when keeper Steve Banks was stretchered off after a collision with a Wimbledon player.
Aidan Davison came on but soon found himself picking the ball out of the net within minutes when Wimbledon equalised on the half hour mark.
Shipperley tested him with a firm drive. Davison was more than equal to it, producing a fine stop, but the ball fell kindly to David Connolly and he made no mistake by drilling the ball home.
Less than a minute later, Bradford had their noses in front again when Standing curled a superb 20-yard shot beyond Davis' reach and into the top corner.
City had a great chance to extend their lead with four minutes remaining in the first half. Standing picked up the loose ball, ran at the Wimbledon defence and released Facey, but he lacked composure and blazed his effort wide from 14 yards.
And City were made to pay for that miss when they gifted Wimbledon their second goal. Standing attempted to play the ball back to Davison but his pass fell short. Connolly raced on to it like a shot and coolly slotted the ball into the net.
Amazingly, City picked themselves up to take the lead for the third time deep into injury time. Standing fired a low drive from the edge of the box past Davis after the keeper pulled off a top-class save to deny Andy Gray.
After the break both sides continued their search for more goals and they duly came.
This time Wimbledon managed to haul themselves back on level terms, as after 49 minutes Connolly grabbed his hat-trick, toe-poking the ball past Davison.
City's on-loan signings almost created their fourth goal. Facey stretched the visitors' defence when he swung over a fine cross. Harpal Singh met the ball with a powerful header from ten yards, but Davis made a comfortable save.
The Dons then found themselves ahead for the first time in the match after 61 minutes. Again it was Connolly who hit the target with a stunning header from Trond Andersen's cross.
City were now beginning to crack at the seams as Wimbledon threatened to turn the screw and kill off the contest, and it was no surprise when they sealed Bradford's miserable fate in the last minute.
Jermaine Darlington ran into the box, cut inside a defender, before placing a low shot past Davison into the bottom right corner.