City moved breathlessly into the last eight of the JPT after a third straight penalties win at Sheffield United.
Chris Mitchell buried the decisive spot-kick after Jon McLaughlin, playing his first game of the season, had saved three penalties in the tensest of shoot-outs.
City had two great chances to take an early lead with headers.
First Ross Hannah nodded over from Jack Compton's inviting cross. Then Steve Simonsen athletically denied Craig Fagan from a centre by Hannah.
Chris Porter blazed behind for the Blades but they made the Bantams pay for those early missed opportunities with a thumping Matt Phillips strike after 27 minutes.
But City equalised five minutes before the break with an even better effort from Michael Flynn, the skipper's fifth goal of the season - and the team's first for four games.
The Bantams more than matched their higher-level opponents and pressed at the start of the second half. Both centre halves went close from Chris Mitchell's corner as the visitors hunted a second.
The game remained open but could not find a winner so once again it was down to the lotteries of penalties. And once again, City pulled out the winning ticket as they had done against Sheffield Wednesday and Huddersfield.
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