But Tony Pulis introduced experienced players Ricardo Fuller and Matthew Etherington just after the hour-mark and the dynamics of the match changed dramatically.
Etherington supplied the first goal of the comeback with a corner that Danny Higginbotham nodded home in the 75th minute and then got his own goal three minutes later to level the score at 2-2.
Stoke then skipped away when Fuller netted in the 80th minute before Blackpool equalised a minute later through Ben Burgess.
Just as everybody thought the game was over, another twist presented itself when Andy Griffin scored deep into stoppage time to send the Potters through to the next round.
Stoke boss Tony Pulis lauded his players for never giving up throughout the entire contest.
“We kept going and created loads of chances in the last 25 minutes,” he said.
“While the substitutes played a part the others who played a full 90 minutes, like Andy Griffin were smashing. I am very pleased for Andy, although Blackpool deserve credit as they played a lot of good football."