Matt Taylor's lot were the better side for large spells against the Bantams, and they will feel they were worthy of at least a point.
However, a familiar lack of ruthlessness coupled with some rotten luck resulted in a smash-and-grab victory for the visitors.
Walsall had George Miller and Conor Wilkinson spurn gilt-edged opportunities in the first half, with Derek Adams' Bradford leading at the break thanks to Matthew Daly's deflected effort.
Miller would finally end his long-running drought in the second half, although he did not know too much about it, and the Saddlers pushed for a winner.
But instead, a Zak Mills handball saw the Bantams awarded a penalty, which was emphatically tucked away by Cook.