Goals from Potters pair Ashley Phillips and Tom Cannon threatened to force a penalty shoot-out as the Saints blew a two-goal lead following a Taylor Harwood-Bellis header and an Adam Armstrong spot-kick.
Defender Bree prevented a new low in a miserable season so far for the bottom club by firing home from distance in the 88th minute at sparsely populated St Mary’s.
Southampton were fortunate to reach this stage as only Yukinari Sugawara’s goal-line clearance stopped Stoke substitute Million Manhoef from completing the turnaround minutes earlier.
Having picked up just one point from nine league games since promotion, Russell Martin called his side’s “most important” game of the season.
The Saints boss, who served a touchline suspension after picking up a third booking of the campaign, made six changes to the starting XI that started Saturday’s 1-0 loss at Manchester City, while Stoke’s nine changes include new starts in this 17-man competition – England Under-18 internationals Saul Sidibe and Jayden Dixon.
Southampton midfielder Joe Arribo tested Potters goalkeeper Jack Bonham during a sluggish start to the game before the home side got a breakthrough in the 19th minute.
Mateus Fernandes took a corner from the left and former Stoke loanee Harwood-Bellis easily eluded Phillips’ marker to nod home.
Manager Martin, who was watching the game from the top of the empty stand on the opposite side of the pitch from the technical areas, saw his hosts extend their advantage 10 minutes before the break.
After initially appearing to be pulled by the shirt, teenage Potters defender Dixon fouled Sugawara in the area after being taken out, allowing Armstrong to calmly find the right angle from the spot to grab his first goal since the play-off final win for Championship in May against Leeds.
Stoke arrived in Hampshire just a point above the second-tier relegation zone after just one win from seven games since the appointment of 36-year-old Spain head coach Narcisse Pelach.
The away side initially offered little in attack before halving the deficit in the final minute of the first period when Tottenham loanee Phillips redeemed his role in the opener in spectacular fashion.
As Southampton struggled to deal with Eric Bocat’s free-kick in the box, the 19-year-old curled an impromptu volley into the bottom left corner to register his first senior goal after the ball deflected off Sugawara and fell behind him.
Stoke, whose only win under Pelach was a 6-1 rout of Saints’ bitter rivals Portsmouth at the start of the month, stunned the hosts by equalizing in the 54th minute.
Junior Chamadeu’s incredible effort from the right took a heavy touch from Bree and flew to the back post where Cannon fired high into the roof of the net.
With the danger of spot-kicks looming, Saints breathed a sigh of relief when Sugawara’s alertness stopped Dutch striker Manhoef heading home five minutes from time.
Bree then spared his side embarrassment, firing into the bottom left corner from around 25 yards before the home side held on through the eight minutes of stoppage time.