Nahki Wells, Rory McArdle and Carl McHugh scored for the hosts at a raucous Valley Parade, with Andreas Weimann replying for Villa, as the Yorkshire club closed on a first major final since their FA Cup success in 1911.
Bradford have already accounted for Wigan Athletic and Arsenal in this season’s competition and are bidding to become the first team from the English fourth division to reach the League Cup final since Rochdale in 1962.
The return leg will be played at Villa Park on January 22.
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