Both sides showed plenty of attacking intent in a lively first half and it was a surprise the opening 45 minutes ended goalless.
But Bradford scored just 47 seconds after the interval when fine play by Garry Thompson set up Ritchie Jones to side-foot a perfect shot low inside Chris Neal's left-hand post from 16 yards.
Vale fans were incensed in the 53rd minute when Jennison Myrie-Williams was booked for diving after he looked to have been tripped in the penalty area by Carl McHugh.
And it turned out to be a big call by referee Darren Drysdale as the unmarked Craig Forsyth tucked a 14-yard shot inside Neal's right-hand post following more excellent work by Thompson just two minutes later.
Vale boss Micky Adams reverted to three at the back and pushed skipper Doug Loft further up the pitch in an attempt to get back into the contest.
But the nearest they came to a consolation was a fierce shot by Myrie-Williams which the impressive Jon McLaughlin safely gathered nine minutes from time.