Out-of-form Bradford struck first at Walsall before being pegged back by a header from Neil Emblem.
They took the lead with a fierce Steven Schumacher free-kick but from then on in it was backs against the wall stuff, with keeper Paul Henderson starring.
He made three outstanding saves from Walsall striker Matty Fryatt, before Paul Merson's cross found Emblem.
Both sides had chances to win but City debutant Marc Bridge-Wilkinson shot wide and Simon Osborn was off target.
Walsall: Murphy, Wright, Emblen, Roper, Aranalde, Surman (Merson 45), Osborn, Standing, Wrack (Daryl Taylor 49), Leitao, Fryatt.
Subs Not Used: Kris Taylor, Bennett, Coleman.
Goals: Emblen 72.
Bradford: Henderson, Swift, Atherton, Bower, Armstrong, Bridge-Wilkinson, Schumacher, Crooks, Muirhead (Bentham 62), Windass, Cooke.
Subs Not Used: Ricketts, Forrest, Morrison, Symes.
Booked: Bentham, Cooke.
Goals: Schumacher 20.
Ref: M Cowburn (Lancashire).