Jon McLaughlin saved Evan Horwood’s spot-kick to earn City another dramatic win on penalties in the Johnstone’s Paint Trophy.
The Bantams edged Hartlepool 3-2 in the shoot-out after the game had finished goalless.
McLaughlin had made three important first-half saves to keep out Hartlepool.
McLaughlin, one of the six starters from Saturday to keep their place for City, beat away a fierce volley from Simon Walton after 14 minutes.
He also denied on-loan Middlesbrough striker Charlie Wyke with the best save of the lot from his 27th-minute curler.
And right on half-time, McLaughlin was equal to Ryan Noble’s blast at his near post.
City, playing 4-3-1-2 again, matched their League One hosts in terms of possession but had not tested home keeper Scott Flinders. Garry Thompson fired high and wide after being set up by Alan Connell.
Ritchie Jones made his first appearance of an injury-delayed season. And he almost had a goal against his old club with City’s first real effort after 57 minutes but Flinders tipped over.
As City stepped it up, Jones fired over from another Thompson and Connell link-up and James Hanson headed wide from close range.
McLaughlin saved from Wyke and Flinders denied Nahki Wells, who had come on for Hanson midway through the half.
City nearly snatched it four minutes from time when Thompson’s cross was headed on to the bar by Ricky Ravenhill.