City were without a league win in 16 games but looked like they were on course for all three points when they led the below-par Bantams 2-1 at the break.
But the visitors failed to capitalise and paid the price when Bradford grabbed three goals in the second-half to give them a much-needed win in their battle against relegation.
Nicky Law's men certainly deserved to win but the Potters showed enough at times to suggest that they may still have what it takes to stay in Division One.
The visitors settled quickly on the greasy surface and opened the scoring in the ninth minute.
Ex-Mansfield Town marksman Chris Greenacre swung over a cross from the right.
Chris Iwelumo timed his jump perfectly to flick the ball across the face of the goal before Petur Marteinsson stuck out his leg to stab his close-range effort into the net.
Makeshift striker Andy Gray saw his shot blocked as Bradford tried to hit back.
Andy Todd had a chance to level when the ball cannoned off Peter Atherton's leg and landed at his feet just outside the box but the Scot failed to keep his shot down.
However the home side hauled themselves back into the match when referee Graham Laws awarded a penalty after Sergei Shtaniuk was adjudged to have held Robert Molenaar inside the penalty area on 20 minutes.
Gray stepped up to rifle the spot kick low into the bottom right corner beyond the dive of former Bradford team-mate Steve Banks.
Bradford now had the bit between their teeth and put Stoke under pressure.
Defender Guss Uhlenbeek had two shots blocked before Molenaar tested the keeper with a straight drive.
But, just as Bradford were threatening to dominate, Stoke caught them cold with their second after 24 minutes.
Lewis Neal crossed the ball into the danger area and found Karl Henry who swooped to score with a low header from 12 yards.
Todd should have brought Bradford back on equal terms just after the half hour mark but he failed to hit the target with his outstretched boot at the back post.
After the break, both sides showed plenty of effort and commitment but it was Bradford who turned the game on its head with two goals in four minutes.
Lewis Emanuel delivered a fine cross, Gray poked the ball goalwards before it rebounded off James O'Connor and went over the line.
After 70 minutes Bradford grabbed the lead.
This time Wayne Jacobs supplied a superb cross from the left that led to Clause Jorgensen planting a firm header from eight yards into the corner.
Stoke were clearly shocked but they should still have drawn level when sub Peter Hoekstra blazed over the bar from only 12 yards.
It came as no surprise, however, when Gray added his second and Bradford's fourth in the dying minutes after cutting inside a defender and drilling a low shot inside Bank's near post.
Bradford boss Nicky Laws, said: "We knew if we matched them for effort and endeavour we had too much for them and we would win the game.
"It could be a really significant result for us, as it puts eight points between us."