After a goalless first forty-five minutes Keith Bertschin's side took the lead on 74 minutes through DJ Campbell.
Blues secured the three points when they doubled their lead just five minutes later through Cameron Jerome.
Blues: Legzdins, Howland, Price, Tebily, Campion, Nafti, Wright, Danns, Jerome, Forssell, Campbell. Subs: Birley, Dicker, Aluko, McPike, Kavanagh.
Bradford: Saynor, Swift, Hurrell, Mitchell, Ainge, Clarke, McGuire, Penford, Brown, Osborne, Barrau. Subs: Morgan, Higgins, Taylforth, O'Brien, Bellamy.