Bradford suffered conceding the first goal, Jon Nurse firing home after 27 minutes.
The only goal came when the Bantams failed to clear Gavin Tomlin’s corner and the ball fell to Nurse, who drove a powerful low shot into the net.
It means the Bantams have picked up just one point from their first four matches in League Two.
Bradford had earlier seen Jack Compton’s shot hit the bar.
The hosts dominated the second half but were denied an equaliser when Chris Lewington blocked Ross Hannah’s effort.
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