Villa must reproduce their dramatic 1994 comeback against Tranmere Rovers if they are to reach the Capital One Cup final.
Paul Lambert's young side became Bradford City's latest victims as the Bantams continued their cup adventure by establishing a two-goal advantage in the first leg of the semi-final.
The Yorkshire outfit led at half-time through Nahki Wells and doubled their advantage through Rory McArdle in the 77th minute.
And although Andreas Weimann reduced the deficit, the home side grabbed a third goal through Carl McHugh on 89 minutes.
Despite the setback, though, Villa will not be totally despondent after creating enough chances to have won comfortably.
The visitors were on top for long periods and, significantly, home keeper Matt Duke was voted man of the match.
The game opened at a frantic pace and there could have been goals at either end during a blistering first 10 minutes.
Wells twice went close for the home side, seeing one shot blocked and another saved by Shay Given, while skipper Gary Jones fired wide from the edge of the penalty area.
But Villa looked dangerous every time they moved forward.
Charles N'Zogbia had a fierce left-footer parried by Matt Duke, Christian Benteke headed over from Barry Bannan's corner and an N'Zogbia drive deflected for another flag kick.
There was no let-up in the tempo, either.
Benteke was narrowly wide with a header from another Bannan corner before N'Zogbia made a forceful run before unleashing a low shot which was well held by Duke.
Then Fabian Delph's superb through ball sent Benteke racing through the left-hand channel, only for the striker to fire against Duke's legs as the keeper raced from his line.
But in the 19th minute the home side grabbed the lead with an opportunist goal.
Zavon Hines 25-yard drive took a deflection in a crowded penalty area and the ball ran loose to Wells, who sent an angled shot with the outside of his right boot beyond Given's reach and into the far corner.
Villa responded with another strong N'Zogbia surge, followed by a low shot which was held by Duke - and the keeper did even better to tip Benteke's 22-yard drive away for a corner.
Given came to Villa's rescue on 35 minutes, though, keeping out a Hines drive with his body whena second Bradford goal looked likely - and two minutes later Delph cleared off the line when James Hanson met Gary Jones' corner with a firm downward header.
Even so, the visitors should have been level just before the interval, Gabby Agbonlahor's thundering drive being pushed away by Duke after N'Zogbia had set up the chance with a wriggling run along the byeline.
Within a minute of the resumption, Duke raced out to save from Agbonlahor at the expense of a corner, and the keeper then produced a couple of reflex saves in quick succession.
First he dived to push away Benteke's header from an inviting cross from Bannan, and that was quickly followed by an instinctive block to keep out Agbonlahor's left-foot volley.
Benteke tried his luck with a right-foot volley when the ball reached him beyond the far post in the 62nd minute but his effort cleared the bar.
And Darren Bent, who had replaced Agbonlahor, missed a glorious chance in the 67th minute, heading over an open goal after Duke had been unable N'Zogbia's stinging drive.
The club's record signing was injured as he fell, needing treatment before he could continue.
Bradford had hardly been in the game as an attacking force in the second half but in the 77th minute they doubled their advantage.
Wells had just seen a drive deflected for a corner and when the Bantams maintained their momentum, McArdle met a Jones cross with a header which left Given helpless as it flew inside the near post.
It could have become worse straight after when Hanson's header struck the bar.
And although Weimann threw Villa a lifeline when he chased Benteke's flick-on to lift the ball over Duke, there was a sting in the tail when McHugh headed in an 89th-munte flag-kick from Jones.
Bradford: Duke; Darby, McArdle, McHugh, Good; Hines (Turgott 66), Doyle, Jones, Atkinson; Hanson, Wells. Unused subs: McLaughlin, Ravenhill, Reid, Jones, Hannah, Connell.
Villa: Given;Lowton, Clark, Baker, Bennett; Bannan, Delph; Weimann, N'Zogbia, Agbonlahor (Bent 57, Burke 85);Benteke. Unused subs: Guzan, Ireland, Stevens, Lichaj, Carruthers.