Walters and Tuncay put Stoke in command before half-time with headed goals in the 26th and 37th minute but the Premier League side were forced to endure a nervy last 10 minutes thanks to Steve Leslie’s 79th minute goal.
Tony Pulis’ side held on for the win but whether Asmir Begovic will be heading with them along the road to Wembley remains to be seen.
The Bosnian was not included in tonight’s squad, leading to speculation the goalkeeper is about to leave the Britannia Stadium, with Chelsea among the reported suitors.
His absence provided all of the pre-match talk but Stoke’s players did not appear disturbed by it on the pitch.
Walters, who arrived from Ipswich last week, got on the end of a cross from Matthew Etherington to send a glancing header beyond goalkeeper Chris Neal in the 26th minute.
This time there was no dispute about Walters’ effort. He thought he had equalised in stoppage time against Tottenham on Saturday only for referee Chris Foy to allow play to continue.
Shrewsbury suffered a further blow in the 37th minute and again Etherington was the provider.
The midfielder’s delivery into the area was met by Tuncay and for the second time in the space of 11 minutes Neal was beaten by a header.
Whelan thumped in a shot from distance Neel did well to parry as Stoke kept up the pressure and it continued after the break.
Etherington surged forward in the 54th minute and drove in a shot that caught Neal on the hop, with the goalkeeper grateful to turn it around the post for a corner.
Shrewsbury were finding it difficult getting out of their own half and Whelan was off-target from distance before Michael Tonge dragged a shot wide of the post.
Pulis decided to shake things up and brought on Ricardo Fuller for Tuncay in the 67th minute with Chelsea to come on Saturday.
The sight of Fuller coming on the pitch must have been slightly un-nerving for Shrewsbury, given he scored against Tottenham
However to their credit they pulled a goal back in the 79th minute through Leslie, who headed in at the back post.
Leslie took full advantage after Ryan Shawcross and then Nash failed to deal with a routine cross from Sean McAllister.
Walters should have restored Stoke’s two-goal advantage in the 85th minute but he somehow clipped his close-range effort wide of the post.