League One Bradford had provided one of the greatest shocks in the competition's illustrious history in the previous round when they came from two down to defeat Premier League leaders Chelsea 4-2 at Stamford Bridge.
Sunday's fifth-round encounter at Valley Parade lacked the thrilling drama of that match, but it was still another memorable victory for a side who have become accustomed to ousting top-flight opposition in the cup competitions.
It also provided a headache for British TV executives, who had controversially opted not to show the match live - despite Bradford's heroics in round four.
O'Shea put through his own net in the third minute when he unwittingly diverted Billy Clarke's shot past Vito Mannone, before former Sunderland man Stead capitalised on a poor clearance from Adam Johnson to fire low under the body of the visiting goalkeeper shortly after the hour mark.
Sunderland, without the rested Jermain Defoe, struggled to create clear goalscoring opportunities on a difficult playing surface, and Bradford were able to comfortably see out the victory and book their spot in the last eight of the FA Cup for the first time since 1976.
Bradford have never lost at home in a cup competition under manager Phil Parkinson, and that sequence was extended to 12 matches as they toppled a Premier League side for the second time in just over three weeks.
Sunderland made six changes from their midweek defeat at home to QPR and found themselves behind early on.
The visitors failed to clear Filipe Morais' free-kick from the right and the ball fell to Clarke, whose wayward shot took a wicked deflection off O'Shea and flew past Mannone.
After a stoppage to allow Danny Graham and Rory McArdle to receive treatment following a nasty clash of heads, Bradford went close to a second goal in the 16th minute when Stead's glancing header from James Meredith's cross flashed across goal and just out of reach of James Hanson.
Sunderland felt they should have had a penalty two minutes later when McArdle challenged Steven Fletcher as he prepared to shoot, but referee Kevin Friend waved away the vociferous appeals.
The game continued to ebb and flow, Seb Larsson seeing a shot deflected over before Clarke brought a smart stop out of Mannone following a surging run.
As Sunderland went in search of an equaliser, Bradford goalkeeper Ben Williams got down low to his left to keep out Patrick van Aanholt's drive six minutes prior to the interval.
Goalmouth action was scarce at the start of the second half, before Johnson's mistake allowed Stead to double the home side's advantage after 61 minutes.
Johnson's weak clearance from the byline failed to clear Hanson on the edge of the area and his header found Stead, who controlled the ball before firing in a low effort that squirmed under Mannone and over the line.
That kept up Stead's record of having scored in every round of the FA Cup that Bradford have played in this season, as the League One side created another magical FA Cup memory, and moved one step closer to a dream Wembley final.
