The winning goal came against the run of play in the 37th minute when Vale's leading scorer Tom Pope intercepted a headed back-pass from Bantams skipper Gary Jones, beating 'keeper Jon McLaughlin with a left-footed shot from just inside the penalty area.
Bradford, unbeaten in their previous five league and cup matches, dominated the game but failed to find a way through a strong Vale defence in which Clayton McDonald and John McCombe were outstanding.
The visitors also had goalkeeper Chris Neal to thank for two fine saves in stoppage time as Bradford launched a late assault.
First he turned a 20-yard shot from Bermudan international striker Nahki Wells over the crossbar before then stopping James Hanson's header on the goalline.
