Bradford, who had already disposed of top-flight Wigan Athletic and Arsenal, took the lead when Nahki Wells scored from close range in the first half before Rory McArdle doubled the advantage after the break.
Villa squandered several good chances with substitute Darren Bent guilty of arguably the worst miss, heading over an open goal in the second half before Andreas Weimann pulled a goal back late on for the visitors.
"You are playing against a class team, you need to be on your game," Bradford goalkeeper Matt Duke told Sky after a superb individual display.
"We've got an even bigger challenge ahead of us now."
Teams from the bottom tier of English professional football playing in cup finals is almost unheard of but buoyant Bradford will fancy their chances such is youthful Villa's poor form at the moment.
Villa manager Paul Lambert made four changes to the team which beat Ipswich in the FA Cup on Saturday with Christian Benteke, Weimann and Gabriel Agbonlahor spearheading the visitors' attack.
The visitors' best chance arrived just before the break when Charles N'Zogbia beat his man on the right flank and pulled it back for Agbonlahor who rifled in a shot from close range that Bradford keeper Duke did well to beat away.
The Premier League side looked brighter after the break and Duke was called into action early on, producing a series of good saves to deny first N'Zogbia then Benteke and Agbonlahor.
Striker Bent was a second-half substitute for Agbonlahor and within minutes of coming on, he wasted the visitors' best chance when he headed over from five metres after Duke parried a shot from N'Zogbia.
Their celebrations were short-lived as McHugh rose powerfully in the area to head home Bradford's third.
"Set pieces are a vital part of the game and
