An early own goal by John O’Shea saw the Black Cats get off to a nightmare start, while Jon Stead scored for the fifth successive round in the second half to complete another cup upset for the Bantams.
The famous victory was witnessed by the club’s biggest home crowd for more than 50 years, with 24,021 people turning up to cheer on their heroes.
Phil Parkinson’s side will find out who they play in the sixth round of the competition in Monday’s draw.
Bradford produced one of the greatest cup upsets of all time in the previous round when they beat Premier League leaders Chelsea 4-2 at Stamford Bridge. They also managed to reach the final of the Capital One Cup two seasons ago, losing to Swansea City.