The 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 score within four minutes to send the Bees through to a meeting with Southend.
Fourth-tier Rotherham are through to face Aldershot after a 3-0 win over 10-man Notts County.
Oxford also represent League Two in the next round after they lined up a clash against Sheffield United by seeing off Accrington 2-0.
Blue Square Premiership 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.