Stoke's main attacking threats came from Pugh, Fuller's counter-attacks and inevitably Rory Delap's longthrows, but neither keeper was overly tested in the first half.
Asamoah Gyan regained the lead for Sunderland after the break, but the visitors sat back and finally buckled under a barrage of longthrows and set-pieces, as two Jermaine Pennant free-kicks set up Huth to score twice in the last seven minutes and seal a remarkable recovery.
The first touchdown of the game, a 13-yard strike over the middle of the field to Boldin, showed the touch Flacco had long suggested in his throws but rarely showed consistently until these playoffs.