It was an improbable victory given that the Premier League side found themselves two goals down inside 47 minutes.
Related ArticlesArsenal 2 West Bromwich Albion 0Leeds United 0 Liverpool 1Peterborough 2 Newcastle 0Win Stoke v Man Utd ticketsSport on televisionBut the introduction of Matthew Etherington and Ricardo Fuller made all the difference with both players find the target in a rousing comeback.
Stoke scored three times in the space of five minutes only for Ben Burgess to level matters.
It looked as though the tie was heading for extra time but Griffin's individual effort broke Blackpool hearts.
The Championship team shaded it in the first half and there was a scare for Stoke after 15 minutes when Charlie Adam spotted Burgess racing into the area.
The delivery was inch perfect and Burgess's header came back off the post as the assistant referee raised his flag.
Play switched down the other end and two minutes later Liam Lawrence saw his inswinging free-kick go narrowly over the bar and nestle on top of the net.
Stoke found themselves on the back foot after 26 minutes but Burgess dragged his effort wide of the post.
Adam was beginning to pull the strings in midfield and tried an audacious shot from the halfway line after 30 minutes that just cleared the bar.
Blackpool almost made the breakthrough five minutes later when Jay Emmanuel-Thomas got on the end of a Joe Martin cross, only to send his header over the top.
The visitors went ahead in the 40th minute with an emphatic finish from David Vaughan after he had been set up by Adam.
Blackpool increased their lead 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.
Clarke had won the corner after his effort in front of the posts had been parried by the goalkeeper.
He wheeled away in delight after finding the target and Stoke now faced an uphill task to get back in the match.
Stoke were then awarded a penalty in the 56th minute after Tuncay was bundled over by Alex Baptiste and Ashley Asthma.
Lawrence stepped up only to see his effort turned superbly away by Gilks, who had replaced Paul Rachubka in the Blackpool goal.
Stoke increased the pressure and Tuncay saw his 25-yard shot blocked by Gilks before Beattie fired over the bar from inside the area.
Tuncay should have pulled a goal back only to clear the bar when in a great position.
But the home side got their reward in the 75th minute through Danny Higginbotham who got on the end of an Etherington corner to head home.
Three minutes later Etherington equalised with a crisp finish after Fuller had set up the opening.
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 Burgess pulled them level a minute later.
However, Stoke secured their passage into the fourth round deep in stoppage time when Griffin raced forward and his shot beat Gilks.
Stoke City: Simonsen; Griffin, Higginbotham, Cort, Wilkinson, Lawrence, Soares (Etherington 64), Pugh, Arismendi (Tonge 46), Beattie (Fuller 64), Sanli.Subs: Sorensen, Shotton, Dickinson, Kitson.Booked: Griffin.Goals: Higginbotham 75, Etherington 78, Fuller 80, Griffing 90.Blackpool: Gilks; Baptiste, Eastham (Eardley 83), Edwards, Vaughan, Martin, Emmanuel-Thomas (Bouazza 90), Bangura, Adam, Clarke, Burgess.Subs: Halstead, Crainey, Southern, Ormerod, Euell.Booked: Adam.Goals: Vaughan 40, Clarke 47, Burgess 81.Referee: J Probert.