James Hanson cancelled out Christian Benteke's opener for Villa and although Andreas Weimann's 89th-minute goal gave the hosts a 2-1 win, it could not stop Bradford from qualifying for a first major final since they won the 1911 FA Cup.
League Two side Bradford, who had previously accounted for Arsenal and Wigan Athletic in the competition, become the first team from England's fourth level to reach the League Cup final since Rochdale in 1962.
"It's dreamland," Bradford manager Phil Parkinson told Sky Sports.
"We said we had a chance to make history and we've done it. The lads were absolutely fantastic, and what it means for the club and the city is absolutely tremendous.
"I think we could fill Wembley on our own. To win it might be going too far, but to get to Wembley is great for us."
The biggest game in the Yorkshire club's modern history will occur at Wembley Stadium on February 24, when they will face either Chelsea or Swansea City, who resume hostilities on Wednesday with Swansea 2-0 up from the first leg.
For Paul Lambert's Villa, it was the latest embarrassment in a disappointing season that has seen them thrashed 8-0 by Chelsea and slip to within one place of the Premier League relegation zone.
"That is the worst day of the season. We had two chances to do it and haven't done it," said the Villa manager.
"We've lost four goals from set-pieces over two games, which is not good enough. I am embarrassed. We will never have a better chance to reach the final."
Lambert had hailed Charles N'Zogbia's performance in Saturday's 2-2 draw at West Bromwich Albion and the French winger was at the fore as the hosts made a storming start on a freezing night in Birmingham.
Matthew Lowton headed a knock-down from the Belgian over the crossbar in the sixth minute, while Benteke directed a header straight at Bradford goalkeeper Matt Duke 10 minutes later.
Villa took the lead in the 24th minute and this time the chance came from the left, with Joe Bennett shaping an inviting cross into the area that Benteke leapt to volley past Duke at the near post.
The halftime whistle would have come as some relief to the visitors, but within 10 minutes of the restart they had reasserted their control of the tie.
As on several occasions in the first leg at Valley Parade, Villa were undone from a set-piece, with Hanson slipping past Ron Vlaar to meet Gary Jones' corner with a header that rocketed into the roof of the net.
The goal sparked delirium on the visiting bench but Hanson spurned a glorious chance to put Bradford three goals up on aggregate moments later.
Weimann revived the tie in the penultimate minute after skipping past Duke on the edge of the Bradford area and rolling the ball home.
But thanks to some desperate defending, the underdogs held on for an unforgettable victory.