Andrew Morrell's 52nd-minute goal condemned Bradford to their fifth defeat in their last seven league matches, while Bury wracked up their fifth straight win with a 1-0 success.
Morrell broke the deadlock after an evenly-fought first half almost devoid of clear-cut chances. Michael Jones saw his shot saved by Matthew Glennon, but the Bradford keeper could not hold on to the ball and it ran free to Morrell to shoot into the empty net.
Bradford surged forward in search of an equaliser, but found the strong Bury defence in uncompromising form.
James Hanson saw his header stopped on the line and goalkeeper Wayne Brown twice denied Gareth Evans before turning a fiercely-struck shot from left-back Luke O'Brien over the crossbar one minute from the end of normal time.
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