The shot-stopper pulled off three super saves to deny Dave Jones' men and produced his best just four minutes from time.
City's defence had been superbly marshalled by skipper David Wetherall but they were finally undone by Nathan Blake's inch-perfect pass into the path of substitute George Ndah.
The Wolves striker left Wetherall in his wake but his shot from just inside the City box was brilliantly pushed away by the impressive Walsh.
The Bantams, who gave home debuts to new faces Andy Gray, Paul Evans and Gus Uhlenbeek gave as good as they got in a lively contest.
Striker Ashley Ward came closest to breaking the deadlock for City when he volleyed over an Evans corner after 52 minutes but Wolves had the better of the clear cut chances.
Midfielder Colin Cameron saw his snap-shot pushed out by Walsh after 33 minutes and team-mate Alex Rae could only watch in agony as his follow-up effort dribbled wide from close range.
Twenty minutes from time Walsh showed his class again to deny Kenny Miller when he volleyed goalward from just eight yards out and the City keeper made it a frustrating day for the visitors when he tipped away Ndah's late effort.
But Wolves boss Dave Jones was still upbeat after the draw.
"We had chances certainly the last one at the end," he said. "If you are going to come away from home and battle I think everybody's disappointed we did not stick it away. On another day we probably would have.
City boss Nicky Law added: "That performance epitomized the players I have got.
"I think the way they conducted themselves over the last three or four months has been nothing short of exemplary.
"I can't praise them highly enough they are a great set of players to work with."