Kevin Phillips became Sunderland's post-war FA Cup record goalscorer with his tenth goal in the competition after ten minutes when sent clear by Sean Thornton.
Phillips had the ball in the net again ten minutes later only to be ruled offside and Julio Arca failed to hit the target with the goal at his mercy as Sunderland belied their lowly league position.
Thomas Sorensen denied Andy Cole with a diving save but the game took a cruel twist early in the second half. McCann robbed Martin Taylor to release Phillips who went clear and beat Brad Friedel only for his low shot to come back into play off the post.
McCann's stunning 78th minute strike restored Sunderland's lead but after Henning Berg had missed a sitter, up popped Flitcroft again to send the tie into extra time.
The added period failed to settle the tie but amazingly Blackburn failed to convert any of their penalties. Phillips scored, Thompson blazed over the bar, Kevin Kilbane made it 2-0 and Andy Cole had his shot saved.
Jody Craddock fired wide but substitute Corrado Grabbi had his penalty saved and although Friedel got his hands to McCann's effort, he could not prevent the ball from crossing the line.