In an even opening it was the Bantams who forced the first effort on goal with top scorer Nahki Wells seeing his effort blocked by Chris Smith on the edge of the area.
Prior to half time, the Minstermen had a glorious chance to open the scoring through Jason Walker but Carl McHugh blocked his effort on the line after rounding Jon McLaughlin.
Midway through the second half both goalkeepers were called into action with McLaughlin denying Matty Blair before Michael Ingham produced two saves in quick succession from Kyel Reid and Andrew Davies.
The breakthrough finally came in the 75th minute courtesy of James Hanson as he powerfully headed home Stephen Darby's cross with the ball squirming between Ingham's legs.
The Bantams wrapped up the points four minutes from time as substitute Garry Thompson capitalised on a slip from Jack O'Connell to race away and fire past the keeper.