The hosts were dominant throughout the encounter but had to wait until midway through the second half before finally grabbing the breakthrough.
Just three minutes in, Rovers mounted a counterattack and Elliott Bennett connected with a rebound that fell to him 10 yards out, but the City defence charged the effort down.
On 23 minutes, Bradley Dack won a corner and, from the ensuing set piece, Blackburn struck the bar twice in quick succession before the visitors eventually cleared.
Although Bradford gradually began imposing themselves on the hosts in the latter stages of the first half, the restart saw Blackburn resume their dominance.
BLACKBURN ROVERS (4-2-2-2): Raya; Bennett, Lenihan (Downing 30'), Williams, Bell; Smallwood, Evans; Dack, Armstrong; Samuel (Payne 65'), Antonsson (Conway 79')
BRADFORD CITY (3-1-4-2): Doyle; Vincelot, Knight-Percival, Kilgallon; Tony; Gilliead (McCartan 64'), Guy (Dieng 72'), Law, Warnock; Poleon (Patrick 64'), Wyke