Ryan Shawcross, the captain, had described the visit of Brighton as their biggest game of the season, with Chris Hughton's team without an away win since November.
Both sides looked to break forward quickly in the early going and had half chances in front of goal, with Maxim Choupo-Moting firing wide from 25 yards for the home side on the quarter hour mark and Glenn Murray sending a flick-on over the bar two minutes later.
Izquierdo served notice of his threat in just the second minute with a fine bending effort towards the top-right corner that Jack Butland did well to parry one-handed.
Badou Ndiaye nearly replied for Stoke before half time. "But the second half was very good".
It was the visitors who had the first chance of the half on 56 minutes. Shaqiri received the ball outside the box, with the Swiss global afforded too much time and space to take a touch before curling a handsome shot out of Ryan's reach into the bottom left corner of the goal. That was the precursor to a stunning ending that started when Jese was felled by Stephens.
Gotze scores on Dortmund return
Schalke refused to buckle, however, and was rewarded for its intensity when Franco di Santo equalized before the half-hour mark. Dortmund leapt up to third after Bayer Leverkusen surprisingly lost 2-0 at home to Hertha Berlin to slip to fifth.
Although Jesé, who had won the penalty in the first place, was rather unimpressed that he didn't get to take the spot-kick.
After the match, penalty hero Mat Ryan said: "It looked like a pretty soft penalty - but I was fortunate to pick the right way and keep it out - and straight after that Lewis Dunk making that tackle and then Anthony Knockaert blocking on the line - it just shows how much character there is in this team".
With the game finely poised at 1-1, Stoke were awarded an injury time penalty kick to grab all three points and move out of the relegation zone.
Albion were eventually grateful for a point at the Bet 365 Stadium.