Walsall secured a first away win since September thanks to Pedro Matias' 73rd minute winner at Valley Parade.
Chris Shuker and Vinny Samways got off to a winning start on their debuts for the Saddlers.
After a slow start to the game Shuker - on loan from Manchester City - and Samways, who has finally received international clearance from Spain, featured prominently in the second half.
Loan signing Carl Robinson gave Colin Lee's men the lead before substitute Danny Forrest restored parity after 62 minutes with a spectacular equaliser.
But Walsall battled gamely and Matias' first goal of the season means the Saddlers leapfrog Bradford in the Division One table to within touching distance of safety.
Bradford dominated the opening exchanges and the game burst into life just before the half-hour mark when the Bantams were denied a goal by goalkeeper James Walker's superb stop from Andy Gray.
After a disappointing first period, Walsall came out firing and it took just four minutes for them to take the lead courtesy of Robinson's second of the season.
Wrack burst down the left channel and lofted a precise delivery into the penalty area that was met by Robinson, who controlled well before side-footing the ball past Aidan Davison from close range.
The home side responded positively and deservedly equalised just after the hour mark.
Jamie Lawrence waltzed past two static Walsall defenders before unleashing a delightful ball into the box.
Forrest had his back to goal but somehow adjusted his body and connected with a stunning overhead kick into the top right-hand
corner of the net.
The Saddlers' responded with a swift counter-attack that unlocked Bradford's backline and Matias was on hand to grab what proved to be the winner.
Shuker found Matias unmarked at the far post with a wonderful ball that left the Spaniard an easy header to earn his side further breathing space away from the relegation zone.
Bradford: Davison, Uhlenbeek, Wetherall, Bower, Jacobs,
Francis, Jorgensen, Emanuel, Lawrence, Ward, Gray. Subs: Walsh,
Cadamarteri, Standing, Forrest, Ekoku.
Walsall: Walker, Bazeley, Roper, Barras, Wrack, O'Connor,
Samways, Robinson, Matias, Leitao, Shuker. Subs: Ward, Corica,
Zdrilic, Birch, Junior.
Referee: R Pearson (Co Durham).