Tough-tackling midfielder Anthony Griffith, making his second Vale debut on loan from Leyton Orient, was treading a tightrope from the sixth minute of the League Two clash at Vale Park after he was booked for a late challenge on Stephen Darby.
And the Bantams were marginally the better side in the scrappy early sparring before the home fans urged their struggling team into greater efforts.
Louis Dodds' shot was deflected narrowly wide with visiting keeper Jon McLaughlin beaten before Tom Pope headed a foot wide from the resulting corner.
Pope looked destined to break his seven-match barren spell in the 32nd minute when his six-yard header drew a superb save from the increasingly busy McLaughlin.
But the visitors came within inches of taking a 49th-minute lead when Chris Neal tipped James Hanson's header against the bar from Carl McHugh's cross.
And the Valiants had another narrow escape on the hour when Richard Duffy cleared off the line from Rory McArdle and then Hanson in a frantic scramble.
Bradford were now the dominant force and Phil Parkinson brought on the speed of Nahki Wells and Kyel Reid in an attempt to take advantage.
But the hosts, with Darren Purse a tower of strength at the back, at least held out for an important point.