Blackpool went ahead in the 40th minute with an emphatic finish from David Vaughan after he had been set up by Charlie Adam and it was 2-0 two minutes into the second half when Billy Clarke got on the end of a corner from Vaughan to send a looping header beyond Steve Simonsen.
Stoke were then awarded a penalty in the 56th minute after Tuncay Sanli was bundled over by Alex Baptiste and Ashley Asthma. Liam Lawrence stepped up only to see his effort turned superbly away by Matthew Gilks, who had replaced Paul Rachubka in the Blackpool goal.
The home side got on the scoresheet in the 75th minute through Danny Higginbotham who got on the end of a Matt Etherington corner to head home.
Three minutes later Etherington equalised with a crisp finish after Ricardo Fuller had set up the opening and the drama continued with Stoke then taking a 3-2 lead in the 80th minute when Fuller scored after linking up with Tuncay.
Blackpool though refused to lie down and Ben Burgess pulled them level a minute later. But Stoke secured their passage into the fourth round deep in stoppage time when Griffin raced forward and his shot beat Gilks.