Tony Pulis' team looked set for an heroic victory when Barry, who fastened on to a flicked header by Emmanuel Adebayor, hooked in the rebound.
But a high-octane contest still ended in controversy when Stoke were denied what looked a perfectly good winning goal seconds from time.
Ryan Shawcross out-jumped Shay Given from Rory Delap's long throw to head home, but referee Alan Wiley awarded a free-kick.
Mr Wiley had earlier sent off Stoke skipper Abdoulaye Faye with another contentious decision and was booed from the field after the final whistle.
The second of three meetings between these sides in 11 days, the other two in the FA Cup, set off at a terrific pace with Stoke calling the tune.
They should have taken a fourth minute lead when Mamady Sidibe shot straight at Given from six yards after Liam Lawrence's free-kick was deflected into his path.
And Roberto Mancini's side dragged 11 men back to defend a barrage of early long throws from Delap, with Stoke really fired up for battle.
Joleon Lescott saved the visitors with a vital clearance when Faye met Lawrence's right-wing corner with a bullet header.
And Mancini, unhappy with what he perceived as Stoke's strong-arm tactics, began to gesture angrily at referee Wiley and the fourth official.
The ferocity of the home side's play relented towards the half-hour mark and Barry miscued a shot wide during a rare attack by the visitors.
But another long throw by Delap had the visitors back under pressure as Robert Huth's header drifted narrowly wide of the far post.
Mancini and his assistant Brian Kidd got in the referee's ear again as the players trooped off at the end of a cut and thrust first half.
The visitors did start the second half better than they did the first and they were given a leg up when Faye got his marching orders in the 54th minute.
Faye appeared to play the ball in halting Adebayor 35 yards from goal, but Mr Wiley, who initially waved play on, produced a red card after consulting a linesman.
The decision incensed the Stoke fans and rallied their players, who reorganized and refused to give an inch.
And they took the lead 18 minutes from time after Adam Johnson miscued an attempted clearance straight into the path of Glenn Whelan.
The former Manchester City trainee struck his 25-yard shot well, but Given will be disappointed with the way the ball squirmed through his grasp and into the net.