The League Two club, who become the first fourth-tier side to reach the League Cup final for 51 years, were put to the sword in Tuesday night's clash at Villa Park but came through the test, with James Hanson nodding home from a Gary Jones corner after Christian Benteke had crowned a dominant opening half from Villa with the opener to cut the Bantams' 3-1 first-leg advantage.
The hosts threatened a late revival as Andreas Weimann grabbed a last-gasp strike but Phil Parkinson's men held on to seal their spot in the final against either Swansea or Chelsea and pile more pressure on under-fire Villa boss Paul Lambert.
Villa had enough opportunities in the opening half-hour to have at least got back on level terms, and the first half-chance fell to Benteke, who climbed above the Bradford defence to meet a cross from N'Zogbia but he directed his header wide.
Another menacing centre from N'Zogbia was headed back across goal by Benteke towards Matt Lowton although he could not keep his header down. But Villa's vulnerability at set-pieces in recent weeks was again highlighted when Hanson headed wide from a Gary Jones free-kick when he should have at least hit the target.
N'Zogbia was supplying a string of dangerous balls across the Bradford box and Benteke sent another header straight at Bantams keeper Matt Duke while Fabian Delph, who had been fortunate not to be booked for a reckless early challenge, was then only inches too high with a powerful 20-yard drive.
Villa defender Ciaran Clark became the first player to be booked for a challenge on Hanson.
Then, after 24 minutes, Villa Park erupted as Benteke gave the home side lead. Left-back Joe Bennett curled the ball in from the flank and the Belgian was first to react as he prodded the ball past Duke.
Stephen Ireland also had the ball in the net shortly afterwards but he had strayed offside.
N'Zogbia continued to ask questions of the Bradford defence and Duke had to be alert to turn over a fierce long range effort. He also reacted sharply to tip Ireland's chip over the bar.
The game followed a similar pattern at the start of the second period with Benteke failing to make full contact on a header from Lowton's centre.
But after 55 minutes Villa's Achilles' heel at set-pieces again proved their undoing as Hanson restored Bradford's two-goal aggregate lead, the striker getting in front of Ron Vlaar to head home Jones' corner and send the 6,500 Bradford fans wild.
Lambert responded by introducing record signing Darren Bent and he set up a low chance for Ireland who stabbed the ball wide at the near post but Bradford substitute Gary Thompson came within inches of making a spectacular entry as his shot thumped against the bar.
The Villa boss brought on a fourth striker in Andreas Weimann and he put Villa ahead on the night after Benteke's flick-on, but Bradford survived the final few minutes to book their place in next month's Wembley final.