Rory Fallon put Swindon in front after 19 minutes with a header from close range from a Miglioranzi cross.
A mix up in the Town defence lead to ex Oxford striker Dean Windass scoring Bradford's equaliser on 33 minutes with a lob over the advancing Heaton.
There was little more action in the first half with the score level at 1-1 going into the half time break.
Bradford took the lead on 63 minutes when Steve Claridge with his socks around his ankles scored from close range against the run of play, as Patrick Collins had just come close for Swindon.
The crowd was calling for Christian Roberts to be bought on, replacing Tony Thorpe who had played a quiet game. Colin Heath also came on to replace Gareth Whalley.
Roberts got off to a poor start when an attempted back pass found Bradford's Dean Windass who was able to pass the ball to Claridge and give Bradford a 3-1 lead after 72 minutes.
The Town End crowd by this time had started to call for Andy King to be sacked, and for the first time this season for the whole board to be sacked.
Rory Fallon pulled a goal back for Swindon on 76 minutes from inside the area for his second goal of the game, but it turned out to be too little too late.
Overall a fairly average game. Swindon look like they will be in a relegation
battle this season and are now in 23rd place on 7 points going into Tuesday nights away game against Doncaster. This was Swindon's 5th defeat in a row, and although Fallon is doing well this season Cureton, Thorpe and Roberts have all failed to give him to support he needs.