Bradford boss Bryan Robson saw the Bantams' mini-revival halted in its tracks by a thunderous strike from Gary Birch.
Robson, appointed managerial successor to Nicky Law at struggling Bradford,
had seen his Valley Parade tenure kick off with a thrilling 3-2 victory over
Millwall last week.
However, there was to be no repeat as Robson saw his side undone by an emphatic 78th-minute finish by Birch, although
midfielder Darren Wrack deserved plenty of credit for his incisive assist.
It took 15 minutes for either side to threaten, Dean Windass firing a free-kick marginally over the Walsall crossbar.
Next to threaten was Tom Kearney who nutmegged Saddlers central defender Ian
Roper on the edge of the box only to be denied a chance to pull the trigger by a
robust intervention from Paul Ritchie.
But the spluttering and misfiring hosts eventually found their rhythm as Steve
Corica left the Bantams rearguard for dead, only to be left shaking his
head in disbelief as Combe saved with an outstretched right boot.
And the Saddlers' sense of frustration deepened moments before the interval
when referee Colin Webster waved away Gary Birch's appeal for a penalty
following a collision with Paul Heckingbottom.
At the other end, goalkeeper James Walker and Ritchie got in each other's way as Gray challenged for a high-bouncing ball on the edge of the box before
Windass arrived to drill into the sidenetting.
Corica was the next to go close when he lashed an effort a whisker over the bar.
But for all the Saddlers' sudden dominance the hosts came close to conceding
in the 63rd minute, although Gareth Farrelly could only stab a Lewis Emanuel
cross from the left over the bar.
And Jason Gavin went closer still with a header which rattled the Walsall bar
from Farrelly's left wing supply.
But it was Birch who finally broke the deadlock as he accepted an inch-perfect pass fired from Wrack and pumped a shot past a helpless Combe.
Walsall: Walker, Bazeley, Roper, Ritchie, Vincent, Wrack, Osborn, Dinning, Corica, Merson, Birch. Subs: Allaway, Aranalde, Leitao, Emblen, Oakes.
Bradford: Combe, Francis, Atherton, Gavin, Heckingbottom, Summerbee, Farrelly, Kearney, Emanuel, Windass, Gray. Subs: Paston, Muirhead, Branch, Bower, Evans.
Referee: C Webster (Tyne & Wear).