Tough-tackling midfielder Anthony Griffith, making his second Vale debut on loan from Leyton Orient, was treading a
tightrope from the sixth minute after he was booked for a late challenge on Stephen Darby.
And Bradford 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 Bradford 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 Vale had another narrow escape on the hour when Richard Duffy cleared off the line from Rory McArdle and then Hanson in a frantic scramble.
The visitors 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 Vale, with Darren Purse a tower of strength at the back, at least held out for an important point.