Stoke duo Mamady Sidibe and Luke Chadwick grabbed the goals to steer their side into the FA Cup fifth round at the expense of Walsall.
Stoke's Sidibe is challenged by Walsall's Westwood
Sidibe opened the scoring when a period of home pressure on the stroke of half-time resulted in him firing in a left-foot shot from 12 yards.
Chadwick cut inside from the right flank and hit a fierce shot into the top corner to double Stoke's lead.
Kevin James tapped in for Walsall but it proved a consolation strike.
Walsall boss Paul Merson's men began to pour forward in numbers and substitute Alex Nicholls was unlucky to see his left-foot shot cannon back off the post.
Stoke were dealt a blow on the hour mark when goalkeeper Steve Simonsen was forced off through injury, but his replacement Ed de Goey preserved the Potters' advantage with a number of notable saves.
Stoke assistant boss Jan de Koning:
"There was still a lot of pressure on us as the game went on but we deserved
to win - at 2-1 it's always tight but it was a great save for Ed.
"He's played so many times for Holland that he has the experience to cope.
"The pressure was there and if they had scored again then of course we would
have had a replay."
Walsall boss Paul Merson:
"We showed them too much respect during the first half and they probably deserved to take the lead.
"But if you analyse things then it was a world-class finish and a world-class save that were the difference."
Stoke: Simonsen (de Goey 60), Buxton, Hoefkens, Duberry, Broomes, Chadwick (Kopteff 77), Brammer, Henry, Sweeney, Gallagher (Sigurdsson 90), Sidibe.
Subs Not Used: Mbuyi, Hill.
Goals: Sidibe 45, Chadwick 49.
Walsall: Oakes, Pead, Gerrard, Westwood, Fox, Wright (Standing 69), Smith, Leary, James, Timm, McDermott (Nicholls 52).
Subs Not Used: Osborn, Gilmartin, Bradley.
Goals: James 51.
Ref: K Stroud (Dorset).