Defender Perry Ng hammers in a free-kick from just outside the box and the Bluebirds have a first goal in five away games.
After 12 without a win and four straight defeats, can the Welsh club hold on for what could be a crucial three points?
Andy Cook's goal looks to have sealed the deal for Bradford as they hunt down the top seven.
The Bantams now 2-0 ahead at home to Tranmere, in a similar boat.
The top two in the table, Leyton Orient and Stevenage, still both lead 2-1 into the final 10 minutes.