Sunderland earned the point they needed to secure top spot in Group F, and with it a home tie in the next round of the EFL Trophy.
Theo Robinson's goal gave Bradford a first-half lead, before Nathan Broadhead levelled just after half-time.
The draw meant the game went to a penalty shootout, and Bradford triumphed 4-2 but it mattered little with Sunderland already through and the Bantams already eliminated.
Go here for all the latest Sunderland AFC news
Here's how James Hunter rated the Sunderland players.
Thorben Hoffmann 7
Made a series of saves to keep Sunderland in the game
Kenton Richardson 6
Did well defensively, and came close to scoring
Frederik Alves 6
Better in his natural position
Ollie Younger 6
Did OK alongside Alves
Lynden Gooch 5
Played at left-back and had a tough night, including a missed penalty in the shootout
Harrison Sohna 5
Too easily beaten for the goal
Luke O'Nien 6
A couple of decent passes to set Sunderland on the attack
Elliot Embleton 6
Excellent throughball for the equaliser
Alex Pritchard 6
Tried to create and he hit the bar right at the death, before missing in the shootout
Leon Dajaku 5
Had a couple of chances but was foiled by the keeper on both occasions
Nathan Broadhead 6
Scored the all-important goal before coming off shortly afterwards
Subs
Will Harris 6
For Broadhead 57mins. Should have scored, but a goalline clearance denied him
Ellis Taylor 6
For Embleton 73mins. Did OK
Carl Winchester 6
For Sohna 73mins. Fresh legs in the final 15 minutes
Not used: Burge, O'Brien, Wright, Dyce
For the latest Sunderland news direct to your inbox, go here to sign up to our free newsletter
