James Bree scores the winner for Southampton. Photo : AFP
And another Premier League team, Brentford, also survived a major scare against second-tier rivals, beating Sheffield Wednesday on penalties.
At St Mary's, Southampton were sailing into the next round after Taylor Harwood-Bellis' header and Adam Armstrong's spot-kick inside 35 minutes.
But goals from Ashley Phillips and Tom Cannon threatened to force a penalty shoot-out until defender Bree rifled home from 25 yards with two minutes left on the clock.
Southampton were fortunate to reach that stage still level as only a goal-line clearance from Yukinari Sugawara stopped Stoke substitute Million Manhoef completing the turnaround minutes earlier.
Saints boss Russell Martin, who was serving a touchline ban after collecting a third booking of the campaign, made six changes to the starting XI which began Saturday's 1-0 loss at Manchester City, leaving the team footing the table with a solitary point from nine outings.
"They (Stoke) defended with big numbers and caught us in a moment on a counter-attack and nearly did again later on in the game," Martin told BBC Radio.
He added: "So the boys came through the moment in adversity and we won the game with some quality from (James) Bree."
In the night's other encounter, Brentford were bossing the show against Sheffield Wednesday after taking the lead through Kevin Schade in the first half.
But Wednesday levelled shortly before the hour with their first effort on target through Djeidi Gassama's spectacular strike.
Brentford could not find a winner in normal time with Mark Flekken their hero, the goalkeeper saving Liam Palmer's penalty to send the hosts through 5-4 after a 1-1 draw.
"I went to the wrong side twice at the start (of the shoot-out)," commented Flekken.
"That doesn't help your confidence in a shoot-out but luckily I saved the last one".
Holders Liverpool are away to Brighton on Wednesday with beaten finalists Chelsea at Newcastle.
Also in action are Tottenham, who host Manchester City, and Manchester United, with Ruud van Nistelrooy acting as interim coach after Erik ten Hag's sacking on Monday.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)
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