Roared on by a fervent crowd, Bradford, who knocked out Premier League leaders Chelsea 4-2 in the last round, were ahead in the third minute when John O'Shea put through his own goal.
Tenacious and relentless throughout, Bradford got a second goal just past the hour mark when their harrying forced Sunderland's England winger Adam Johnson into a mistake and Jon Stead was on hand to slide home a composed finish.
Aston Villa shook off their Premier League woes to progress with a 2-1 fifth-round home win over Leicester City in front of incoming manager Tim Sherwood.
Leandro Bacuna curled in the opening goal in the 68th minute and loan signing Scott Sinclair fired in a second from a tight angle before Leicester's record signing Andrej Kramaric pulled a headed goal back in stoppage time.
Later on Sunday holders Arsenal host Championship leaders Middlesbrough.
OWN GOAL
In Yorkshire, Bradford opened the scoring in the third minute when a free-kick caused havoc in the Sunderland area and Billy Clarke's shot deflected in off O'Shea.
Boosted by the early goal, Bradford suffocated their Premier League rivals with tireless chasing and harassing.
Despite the 37 league places between the sides, Bradford were on top and could have added a second but James Hanson could not convert Stead's teasing header.
Although Sunderland slowly began to assert their authority before the break they were limited to speculative long-range efforts.
The visitors started the second half brightly but it was Bradford who doubled their lead when Stead calmly converted to maintain his record of scoring in every round of this season's competition.
Bradford could have added a third but Billy Knott's blistering strike was well held by Sunderland keeper Vito Manone and the hosts comfortably closed out the game to reach their first FA Cup quarter-final since 1976.
WOEFUL START
After a woeful first half at Villa Park, the tie came alive when Bacuna curled in the opening goal for the goal-shy hosts midway through the second half.
Loan signing Sinclair fired in a second for Villa from a tight angle with his shot squirming through Mark Schwarzer's desperate attempted save.
Leicester's Croatia striker Kramaric pulled a goal back with a powerful header in added time but the visitors, who are bottom of the Premier League, had no time to snatch a replay.
Villa were indebted to goalkeeper Shay Given to keep the scores level in the first period when he made a stunning save to tip a Matty James piledriver around the post.
The experienced stopper said the appointment of former Tottenham Hotspur boss Sherwood had given a boost to the squad who are mired in a relegation battle.
"Everyone's got to prove themselves with the new manager coming on board but it was great to get the victory," he told the BBC. "He was just very positive.
"I've known Tim from the days of Blackburn as a player. He's always a positive guy and he just said go an express yourselves, keep doing the right things and keep getting shots on goal."
