A second-half goal from Eddie Johnson was enough to ensure City gained revenge for their last-minute defeat at Morecambe earlier in the season.
Johnson was restored to his old striking role and he made the most of it by scoring his first goal since September after 54 minutes.
He was on hand to score into an empty net after Barry Conlon's effort was blocked by the goalkeeper following good work by Omar Daley and Joe Colbeck down the left.
City should have been front before then after dominating the first half but Daley missed from a only a yard.
Alex Rhodes and Colbeck had chances to increase the Bantams' lead and Morecambe almost made them pay when Craig Stanley flashed a shot inches wide in injury time.
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