Caretaker boss David Wetherall had hoped his side could follow up Tuesday's shock victory at Bristol City with a long-awaited win on home soil, but despite taking the lead, they failed to keep a clean sheet for the 11th successive game.
Neither side created any real chances in a scrappy first half, but City rode their luck after the interval when Town's on-loan striker Jordon Robertson failed to make the most of two opportunities.
After 55 minutes his ten-yard header was saved by Bantams keeper Donovan Ricketts and a minute later he fired wide from close range with Ricketts stranded.
Robertson then went down claiming a foul by Bradford skipper Mark Bower as he chased a long ball, but his protests were waved away and soon after City striker Billy Paynter headed them ahead.
After 62 minutes Paynter, who scored a stunning volley against Bristol City, guided a looping header over keeper Mark Bunn and the Bradford fans must have felt they were on course for their first home win since December 16.
But just three minutes later, Town drew level after City's defence failed to clear Robertson's cross and 19-year-old midfielder Bradley Johnson drilled home a left-foot shot from the edge of the box.
In City's position, a point would have been better than nothing, but three minutes from time they were hit by a body blow.
Town's busy midfielder Ryan Gilligan pounced on a loose ball on the right and, with City's defence at full-stretch, he picked out striker Kenny Deuchar, who guided the ball beyond Ricketts from ten yards out.