Stoke attacker Jamie Donley powered an effort off the crossbar after the break and Jonny Stuttle had two late chances in stoppage time.
Stuttle blazed his penalty over to send Stoke into the ascendency, before Sam Hornby denied Divin Mubama to level the shoot-out.
Albert Adomah missed the Saddlers' fifth penalty and Stoke goalkeeper Jack Bonham converted the decisive spot-kick to knock Walsall out of the competition.
Only Connor Barrett retained his place from the Saddlers' 1-0 defeat at Gillingham on Saturday, as Mat Sadler made 10 changes to his Walsall XI.

Walsall attacker Albert Adomah grapples for the ball. (Image by Owen Russell)
Harrison Burke, Dan Cox and Vincent Harper made their Walsall debuts while there was a first start for Courtney Clarke following his bright cameos in the first two league games.
Stoke boss Mark Robins also made nine alterations from their 3-1 home win over Derby County in their Championship opener on Saturday.
The hosts enjoyed the early possession and forced Sam Hornby into a smart diving save, after Jamie Donley had pickpocketed Clarke on the edge of the penalty area.
Bosun Lawal also blazed another long-range shot over for the Potters, but Walsall showed positive signs during the opening exchanges.
Barrett's interception deflected into the path of Maher on the inside right channel but the youngster checked on to his left foot and smashed his effort from distance high over the crossbar.
Walsall grew in confidence and they carved out their best chance of the half when Josh Gordon fired Barrett's low cutback into the side netting.
They deservedly went into the break goalless, although Stoke striker Robert Bozenik squandered a great chance on the cusp of half-time when he cushioned his header wide from close-range.
Stoke came even closer after the restart when Donley crashed a powerful strike against the crossbar from the edge of the box following a clever knockdown by Bozenik.

Walsall defender Priestley Farquharson challenging in the air. (Image by Owen Russell)
Sadler brought on triple reinforcements after the hour-mark and replaced Farquharson as a precaution moments later after the defender went down with cramp.
Walsall continued to frustrate their Championship opponents with Jamille Matt coming on for the closing stages and Adomah switching to right wing-back.
Comley produced a really smart display in the centre of the park, extinguishing fires across the pitch time and time again.
The Saddlers struggled to create in the final third during the second period, with Aden Flint coming closest when he glanced Jamie Jellis' chipped cross comfortably wide late on.
Substitute Stuttle had two chances in quick succession during stoppage time. First, Matt pounced on a loose ball to slot the ball into his path and the Bournemouth loanee drilled a low shot which deflected wide of the near post.
Jellis' resulting corner was knocked down to the back post but Stuttle could only stab his finish wide from close-range.
The tie ultimately went to penalties with Matt and Lewis Baker both converting the first penalties for either side.
However, Stuttle blazed over and Donley scored to send Stoke into the lead. Flint kept his composure to keep Walsall in the shoot-out and Hornby plunged to his left to deny Mubama.
Jellis and Bae Junho were both successful with their attempts before Adomah's tame spot-kick was saved by Bonham.
The Stoke goalkeeper then stepped up to score the winner and eliminate Walsall from the competition.
**Teams**
Walsall (3-1-4-2): Hornby; Burke, Farquharson (Flint 74), Cox; Comley; Barrett (Jellis 65), Clarke (Matt 77), Maher (Hollman 65), Harper; Adomah, Gordon (Stuttle 65).
Unused: Roberts, Hancock, Warrington, Browne.
Stoke (4-2-3-1): Bonham; Mears, Phillips, Gibson (Wilmot 63), Bocat; Lawal (Smith 63), Seko (Baker 78); Manhoef (Junho 63), Fawumni, Donley; Bozenik (Mubama 89).
Unused: Fielding, Tchamadeu, Cresswell, Thomas.
**Other details**
Referee: James Bell
Attendance: 8,809 (1,325)