John Egan's strike midway through the first-half was the decisive factor for the visitors as they grabbed their first victory of the campaign.
Fresh off the back of their first League win of the season at Southampton, the Potters gave Karim Rossi a start up front while goal hero Jordan Richardson continued in the midfield quintet.
For Sunderland, first-team full-back and former Manchester United trainee Philip Bardsley was given a run-out as he continues his comeback from injury.
After a tentative start from both sides, the Black Cats had the game's first opening on 14 minutes when Bardsley's cross was met with the head by Egan, but Dale Eve made a decent reaction stop.
Stoke's play lacked direction early on, and Louis Laing had a mazy run through the Potters defence but his cross was blocked behind for a corner.
The visitors took a deserved lead on 24 minutes after a slick move - Craig Lynch beat two defenders before moving the ball onto Laing, who squared for Egan to turn home past Eve.
Lynch then had a chance of his own on the half hour when he found space outside the box but drove his left-footed effort wide.
City's youngsters were struggling to retain possession and their early luck was summed up when Jordan Richardson had a chance to test Jordan Pickford from distance but miscued at the critical point.
They put together their first fluent move of the match on 33 minutes when Michael Clarkson played a clever one-two with Rossi which allowed Richardson some space in the area, but Pickford palmed the shot away and Clarkson couldn't reach the follow-up.
The opening seemed to give Stoke some confidence and the contest was more even in the run-up the half-time, although Sunderland could have doubled their lead when Jordan Laidler scooped his shot over the bar after finding space in the box.
Jadan Hall forced a save for Pickford from 25 yards, and that proved to the last action of a half from which Sunderland certainly merited their advantage.
Laidler nodded wide on 58 minutes after Blair Adams' excellent cross as the Black Cats set off on the same footing after the break.
He then had an even better chance moments later when Adam Mitchell's unerringly accurate cross left him with a header that he will be despairing at how he managed to flick beyond the post.
Stoke weren't offering much incision in the attacking third and could count themselves lucky to be only one down, especially after Laing fired over after fashioning some space 18 yards out.
Rossi had a pot shot from 20 yards as he tried to get some momentum into his side's play, although they had Eve to thank as he kept his side in it when he smothered Laidler's shot.
City introduced James Alabi and Marcel Barrington to try and hasten activity up front, and a couple of wicked Andy Musungu corners tested the Black Cats back line but ultimately came to nothing.
Lynch, a constant threat all night from the left wing, steered a shot wide after another run on 80 minutes.
A bad-looking injury suffered by Laing took the sting out of the closing stages of the game, and although Stoke pressed in the final moments, Sunderland took the points to widen the gap between the two sides at the bottom of Group 2.
Academy manager Dave Wright said after the game: "We were disappointed with the result, but overall quite encouraged by the performance. We thought we deserved something from the game.
"We work on our finishing a lot, but it's a weakness in the team at the moment. We do create chances, but unfortunately we're just not sticking them in the net at the moment."
Stoke City: Eve; Glasgow, Keane (c), Heneghan, Campbell; Hall (Scott 88), Richardson (Barrington 73), Clarkson, Rigg, Musungu; Rossi (Alabi 73).
Sunderland: Pickford; Bardsley (Marrs 79), Egan, Ferguson, Adams; Mitchell, Laing (Knott 88), Reed (c) (Armstrong 50), Trialist, Lynch; Laidler.