Bradford, meanwhile, took full advantage of set pieces when they arrived.
Wells coolly slotted in a shot from inside the penalty area, after Villa failed to clear a corner and a shot from distance was deflected into the Bermudian striker's path.
"It was a good time to get the goal, it put us in a better position," Wells said. "It just gave us the spirit to keep going."
Villa put on striker Darren Bent to replace Gabriel Agbonlahor in the 57th minute, but he wasted a good chance for an equalizer by heading over the crossbar with the goal at his mercy after Benteke's shot had rebounded off Duke.
McArdle then headed home a cross in the 77th minute to give the hosts a two-goal lead before Weimann pulled one back for Villa when he turned the ball home at the far post five minutes later.
That may have been enough to give Villa a clear edge going back home, but McHugh gave Bradford real hope of reaching Wembley when he launched himself at Blair Turgott's cross to plant a hard header into the net.
"We knew it was coming with the set pieces, but we never defended them well at all," Villa manager Paul Lambert said. "We have another chance to retrieve this. We will have to see what happens in a fortnight's time."
In the other semifinal, Chelsea hosts Swansea on Wednesday.
