The contest finished 1-1 after 90 minutes with the Bantams going on to win the penalty shootout 4-2 to pick up the bonus point.
There was little riding on the game for City ahead of kick off as two defeats in their opening two fixtures meant they were unable to qualify for the next round.
Both sides made seven changes from last weekend's FA Cup outings. However, it was a familiar face in the Bantams line-up that put them ahead as Theo Robinson scored with 36 minutes gone for his second goal in as many games.
Nathan Broadhead levelled for the hosts seven minutes into the second half as the sides could not be separated after 90 minutes.
Elliot Watt had his penalty saved as Bradford missed their first spot-kick but goalkeeper Sam Hornby was on hand to keep out Alex Pritchard's effort.
The Bantams scored their next four penalties to win the shootout, as the Black Cats Lynden Gooch saw his spot-kick saved by Hornby.