The Tykes took the lead just before the 20th minute when Eliot Simoes slid the ball into the bottom corner.
Affairs were levelled through Tyrese Campbell but the away side went into the break ahead when Dominik Frieser poked the ball past Adam Davies from close range.
However, at the start of the second half, a fumble from a cross by Walton fell straight into the path of Tommy Smith who then had no issues of smashing the ball into the back of the net.
With under half an hour to go, Nathan Collins was sent off for Stoke for an off the ball incident with Frieser but if anything it was Michael O'Neil's side that could have ran away with all three points.
In the final ten minutes, they had three glorious chances to do exactly that,t but they failed to capitalise on any of them
Story of the game
After an even start, it was the Tykes that created the first opportunity of the day in the ninth minute when a cross from the right found Cauley Woodrow unmarked at the back post, but his volley was well blocked at the near post by Nathan Collins.
Then on the 18th-minute mark, the visitors took a deserved lead when on the right-hand side of the box Woodrow slid the ball into an arriving Simoes who from inside the area slotted the ball into the bottom right-hand corner.
After the deadlock had been broken, Barnsley began to control the game as the Potters really struggled to gain any momentum and show any sign of testing goalkeeper Jack Walton.
This was until the 35th minute when Nick Powell cleverly slipped in Steven Fletcher one on one, but his low shot from the right-hand side of the area was kept out by the feet out Walton.
Three minutes later, Romal Palmer had a sign of goal when he latched on to loose pass from out of the back, but his half volley was sliced well wide of Davies's goal.
However, with only a minute of the half left, Stoke levelled when Harry Souttar slipped Campbell in behind the Barnsley high line, and he had the composure to strike the ball past Walton and into the bottom right-hand corner.
The score only stayed this way for a matter of moments though when with almost the last kick of the first period, a cross from the left by captain Alex Mowatt sailed over Soutarr and on to the onrushing boot of Frieser who then guided the ball into the back of the net.
Although, O'Neil's were gifted an equaliser almost immediately after the restart when a Jordan Thompson cross from the left was dropped by Walton and Smith was alive to the loose ball to lash home.
This was the boost that the Potters exactly needed and should have really been ahead in the 54th minute when Powell once again slipped in Fletcher but his curling effort from a tight angle sailed well over the crossbar.
Then just after the hour mark, the tide of the game changed completely when the hosts were sent down to ten men as Nathan Collins received his marching orders for an off the ball incident with Frieser.
With the extra man advantage, Adam Murray's side regained control and six minutes later they had a golden chance to go back ahead when Mowatt fed Clarke Odour on the left-hand side but his half volley caused no problems for Davies.
With the away side piling on the pressure, Davies prevented them from going ahead for the third time when Callum Brittain was released down the right-hand side by Mowatt, but his driven effort was brilliantly blocked by the former Barnsley goalkeeper.
A minute later Brittain tested Davies for a second time when his low volley took a deflection, but the 28-year-old managed to adjust his feet and keep out the effort.
With ten minutes remaining, the hosts had a great opportunity to steal all three points when a Thompson cross from the left was met by James Chester, but he was unable to connect cleanly with the ball as it floated wide of the mark.
Six minutes later the hosts had another chance to snatch the victory through former Barnsley winger Jordan Brown, but his low shot inside the area was fantastically blocked by Michal Helik.
As the game was approaching stoppage time, Soutarr had a final opportunity to win it for his side, but his header from a Thompson free-kick from the left glanced narrowly wide of the right-hand post.
Barnsley fail to capitalise on three points opportunity.
At the break despite only being one goal ahead, the Tykes looked quite comfortable. The Potters had not given them too much to think about defensively and they nullified the threat that they posed going forward very well.
However, with the mistake that has ultimately cost them the win and with chances having gone begging for Brittain and Odour in the second half when the hosts were down to ten men, they will see this an opportunity missed to get themselves their first league win of the season.
Stoke’s home form could become a cause for concern
Meanwhile, for Stoke tonight’s result confirms that they are winless in the last three league games at the Bet365 Stadium after previously losing 2-0 to Bristol City and being held to a 1-1 draw by Birmingham City.
Consequently, the fact that this is the case means that it is the first time that this has happened since they went on an 11 game winless run at the Bet365 Stadium that ran in 2019 from March all the way through to October.
Even though under Michael O’Neill it is known that they have greatly improved and developed since they endured that poor run of form, the Potters will be keen to ensure that they get out of the current home rut that they are currently in.
This is because if it goes on for much longer it could begin to affect the mentality and the confidence of the players when preparing for future games at the Bet365 Stadium.
Star Player: Alex Mowatt
The midfield captain for Barnsley undoubtedly controlled the flow of the visitor's attacks throughout the entirety of the game.
This was, in particular, the case in the first half because he started many of the counter-attacks that caused Stoke’s back three such problems in that period.
Then in the second half, he was more often than not very composed and relaxed on the ball, and when space opened up on the flanks, he played accurate balls into the dangerous areas, it was just a shame for him and his side that they could not make more of the openings.