Walters struck just 100 seconds into extra-time following a miserable, scoreless 90 minutes, and then added a second goal during the closing stages.
The Cardiff defence failed to track him from substitute Michael Tonge’s inswinging corner, and Walters’ header flew past stranded goalkeeper Tom Heaton.
And Heaton could do little to prevent Walters scoring again six minutes from time, as he finished expertly from close range.
Stoke manager Tony Pulis’ decision to make 10 changes at times looked like backfiring as Championship promotion challengers Cardiff enjoyed the lion’s share of possession in normal time.
The Welsh side had frantic injury-time penalty appeals waved away by referee Peter Walton after substitute Michael Chopra went down, before Walters condemned them to a third-round exit.
Neither Heaton nor his opposite number Thomas Sorensen were seriously threatened during normal time when poor skill levels and weak finishing combined to make it a forgettable tussle.
But at least the crowd of 13,600 were spared penalties as Stoke sealed a Molineux appointment with Mick McCarthy’s men later this month.
CARDIFF: Heaton, Blake, Hudson, Gyepes, Naylor, Rae, McPhail (Wildig 39), Drinkwater (Matthews 75), Burke, Parkin (Chopra 64), Keogh.
STOKE: Sorensen, Shotton, Collins, Faye, Higginbotham (Tonge 10), Whelan, Pugh, Diao (Wilson 75), Pennant (Soares 79), Fuller, Walters.
Referee: P Walton (Northamptonshire).