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Bradford, who had already disposed of Wigan Athletic and Arsenal, took the lead when Nahki Wells scored from close range in the first half before Rory McArdle doubled the advantage after the break.
Villa squandered several good chances with substitute Darren Bent guilty of arguably the worst miss of the night heading over an open goal in the second half before Andreas Weimann pulled a goal back late on for the visitors.
It proved to be a brief ray of light on a grim evening for Villa, however, as Carl McHugh added gloss to the scoreline with two minutes remaining.