Bermudian striker Nahki Wells netted for the home side on 19 minutes before McArdle nodded home on 77 minutes.
Despite Andreas Weimann pulling one back for Paul Lambert's troops, Carl McHugh restored the two-goal lead on 88 minutes.
"It's not quite sunk in, it's similar to the Arsenal game (quarter-final), emotions are here, there and everywhere," said McArdle, who joined the Valley Parade club in the summer after two years at Pittodrie.
"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."
Villa Park gaffer Lambert added: "We have another chance to retrieve this. "We will have to see what happens in a fortnight.
"We will be at home and we know what we have to do. We have to play a lot better than that."