The npower League Two side, reinstated to the competition on appeal after initially being thrown out for fielding an ineligible player, held their League One opponents to a 1-1 draw at the end of normal time before they eventually went down 4-2.
Kyel Reid's opener was followed by a Marcello Trotta penalty on the cusp of half-time before a scoring splurge in the added half-hour. Alan Connell put Bradford ahead from the spot four minutes after the resumption only for Trotta, Clayton Donaldson and Harry Forrester to all score with within four minutes to send the Bees through to a meeting with Southend.
Fourth-tier Rotherham are through to face Aldershot following a 3-0 win over 10-man Notts County.
Ben Pringle and Mark Bradley had already scored before Damion Stewart's red card on the half-hour and Daniel Nardiello completed the scoring four minutes from half-time.
Oxford also represent League Two in the next round after they lined up a clash against Sheffield United by seeing off Accrington 2-0.
James Constable and Peter Leven were the scorers.
Blue Square Bet Premier rivals Barrow and Macclesfield must meet again for the right to host Cardiff after a 1-1 draw.
Kieran Charnock put Macclesfield in front in the 19th minute, with Richie Baker levelling 10 minutes later.
- Sports & Recreation
- Marcello Trotta