The Bantams are seven points adrift of the automatic promotion places, and have a six-point buffer over Millwall in seventh.
Billy Clarke broke the deadlock in the 58th minute, with the all-important goal.
But Stuart McCall’s men were not gifted all three points, with chances at a premium in the first half.
It was mid-table Walsall who fashioned the first opportunity as Cypriot international Andreas Makris’ low drive forced Bradford goalkeeper Colin Doyle into a full length dive to turn away.
But the Saddlers needed a clearance off the line from James O’Connor to keep out Alex Jones’ header after Neil Etheridge had failed to gather Tony McMahon’s right-wing cross.
Bradford did grab the all-important goal in the 58th minute when Mark Marshall’s left-wing cross ran free to the unmarked Clarke, who fired into the net from close range.
Charlie Wyke went close to furthering Bradford’s lead while Walsall’s best chance of salvaging a point fell to Kieron Morris, whose close range shot was saved by the diving Doyle.
Bradford: Doyle, McMahon, McArdle, Knight-Percival, Meredith, Marshall, Cullen, Vincelot, Clarke, Jones, Wyke. Subs: Darby, Law, Toner, Dieng, Hiwula, Devine, Cracknell.
Walsall: Etheridge, O’Connor, Preston, Laird, McCarthy, Osbourne, Chambers, Edwards, Moussa, Morris, Makris. Subs: Dobson, Jackson, MacGillivray, Kinsella, Roberts,
Referee: Michael Salisbury (Lancashire)