Nahki Wells coolly dispatched a shot from inside the penalty area following a rebound in the 19th minute and defender Rory McArdle headed home Gary Jones’ cross in the 77th minute to give the npower League Two side an unlikely two-goal lead.
Bradford almost put the tie beyond their top-flight opponents moments later when striker James Hanson headed against the crossbar, but Villa, who spurned a hatful of chances in either half, grabbed a crucial late lifeline through Andreas Weimann before McHugh restored the home side’s two-goal advantage with another header two minutes from full-time.
Like Given, McHugh hails from Donegal and he said: “It’s all a bit of a blur. It’s unbelievable to score against him, with us coming from the same part of Ireland.
“I have watched him play in World Cups for Ireland and it’s a dream come true.
“I was determined to make sure we got the two-goal lead. I didn’t care how I got my head on it.”
Of equal importance was McArdle’s goal and he admitted to being in a state of shock at what had happened.
“It’s not quite sunk in, it’s similar to the Arsenal game, emotions are here, there and everywhere,” he said.
“It’s going to be a tough test ahead but we’ve more than done well enough to build a platform and if we can do that in the second leg, we won’t be far away.”
Bradford’s Bermudan striker Nahki Wells conceded his side are now favourites to reach the final but would prefer it if they remained as the underdogs. “We may well be the favourites now, but we want to be the underdogs,” he said.
“We showed our quality and that we can compete with Premier League teams. We were resilient, it was a tough match and we showed what we are capable of. To have a two-goal cushion is great.
“We would have taken a draw but 3-1 is amazing.’’
Aston Villa manager Paul Lambert was left to lament his side’s failure to deal with balls into their box.
“We are really disappointed. We’re in one now, that’s for sure,” he said.
“We knew the set-pieces were coming, we have not defended them well at all. It’s hurt us and wasn’t good enough.
“We had a lot of the game but their set-pieces. We have another chance to retrieve this. We will have to see what happens in a fortnight’s time.
“We will be at home and we know what we have to do. We have to play a lot better than that.”
Bradford manager Phil Parkinson had said beforehand he would have taken a draw, but was left knowing that his side are on the brink of what would be a quite sensational final appearance.
“We played so well. They had an attacking line-up and left space, so we passed it well. They had chances but so we did we. All round, the lads were magnificent. But let’s not get carried away, we will be respectful and go to Villa Park and do it all again.”
BRADFORD: Duke, Darby, McArdle, McHugh, Good, Hines (Turgott 65), Gary Jones, Doyle, Atkinson, Wells, Hanson.
ASTON VILLA: Given, Lowton, Clark, Baker, Bennett, Agbonlahor (Bent 57), Delph, Bannan, N’Zogbia, Benteke, Weimann, Bent (Burke 85). Referee: Howard Webb