Parkinson's npower League Two side performed more cup heroics in front of another full house to claim a third win against Barclays Premier League opposition in the competition and give themselves a real chance of fulfilling a sensational Wembley dream.
Leading scorer Nahki Wells seized on a rebound to dispatch his 16th goal of the season in the 19th minute and, after a string of missed Villa chances and excellent saves from Bradford keeper Matt Duke, defender Rory McArdle punished Villa with a thumping 77th-minute header.
Bradford almost put the tie to bed moments later when striker James Hanson's header hit the crossbar.
Villa looked to have thrown themselves a lifeline when striker Andreas Weimann bravely turned home Christian Benteke's flick-on in the 82nd minute but Carl McHugh sent Bradford fans into dreamland two minutes from time when heading a third goal for Parkinson's side from another pinpoint cross from skipper Gary Jones.
But Parkinson refused to be swept away by the occasion, saying: "It was important we got the message across to the lads at the end of the game and equally be respectful to Villa because in two weeks' time we've got to go down to Villa Park and do it all again.
"We're absolutely delighted with the way we played, obviously, because from the first minute to the last the lads were tremendous. But equally we know we're only halfway there, we've got a very difficult job in a fortnight's time."