The young Potters ended draw 5-5 with the Londoners, a frustrating outcome after they had taken the lead on three occasions in an action-packed affair.
Adam Thomas cancelled out an early Palace opener before Immanuel Parry put the Potters in front with a powerful header.
The visitors then scored twice in quick succession to take a 3-2 lead before Jordan Richardson leveled the tie just before half-time.
Thomas netted his second after the restart before yet another equaliser. John Marsden then scored a superb 30-yard drive that looked likely to give Stoke victory, but the referee awarded the Eagles a late penalty that was put away to ensure they got a point from the epic encounter.
Stoke captain Jordan Keane came close to opening the scoring early on but his header drifted across goal and just wide of the far post. Richardson then fired over from distance while Keane had to be alert at the other end to block a goal bound shot.
And the Potters had the ball in the back of the net soon after when Richardson's deep free-kick evaded everyone, only to see the goal chalked off for offside. The Eagles then took the lead 19-minutes in, albeit against the run of play, when Appiah crossed the ball to Allasanni at the back post to tap in.
But their lead lasted only two minutes as Stoke made an instant reply through Adam Thomas who won the ball, beat his man and showed great composure to slot the ball past the goalkeeper.
Andy Musungu did well to earn Stoke a corner from which they went ahead for the first time in the game. Lucas Dawson crossed the ball into a dangerous area and Parry got up well to attack it and head into the back of the net.
Thomas and Charlie Ward missed chances to extend Stoke's lead before James Alabi saw his shot saved by the 'keeper following a great solo run from his own penalty box.
These misses proved costly as the visitors leveled 40-minutes in when Inniss headed in from a corner. Palace scored again just two minutes later when Musungu lost the ball to Appiah on the edge of the area and the striker fired past Daniel Bachmann in the Potters goal.
But in a crazy game when the momentum kept changing hands, Stoke leveled to make it 3-3 just before halftime with a third goal in five minutes. Another whipped in corner from Dawson was met at the far post by Richardson whose header bounced up into the roof of the net, to score the sixth goal of the half.
The second period started in equally frantic fashion as Ward shot just wide after a quick breakaway by Dave Kevan's side. Palace missed a great chance to take the lead when Selassa somehow fired over from six-yards, and Stoke made them pay as they took a 4-3 lead on 57-minutes.
Alabi sent a low cross across the box that Marsden couldn't quite reach, but winger Thomas was on hand at the far post to tap in and score his second of the game.
Bachmann made a great save to deny Appiah before Allasanni fired inches wide as the visitors looked for an equaliser. And that duly came on the hour mark when Appiah headed home a corner at the back post, with Bachmann unable to get enough on the ball to keep it out.
Richardson and Alabi shot wide before Marsden restored the Potters' lead with a stunning low 30-yard drive that found the bottom left corner of the net.
That goal appeared to be the winner, but Palace were awarded a penalty after a free-kick was adjudged to have struck a loose hand in the wall. Boatang stepped up and fired past Bachmann to give his side a share of the spoils, although Richardson, Ward and Alabi all missed chances that could have won it at the death for the Potters.
The 5-5 draw brings an end to the season for the Under-21s who have had a disappointing season and finish bottom of Group Two in the Barclays Under-21 Premier League. But at least Dave Kevan will be happy with his side netting five times in their final outing, and putting in a strong performance in a game that they ultimately deserved to win.
Stoke: Bachmann; Keane, Parry, Dawson, Musungu; Hall, Ward, Richardson, Thomas; Alabi, Marsden (Barrington, 77)
Palace: Fitzsimmons; Taylor, Wynter, Inniss, Parsons; Selassa, Parrett, Boatang (Akuruha, 90), Allasanni; Banton (Palmer, 73); Appiah (Henry Francis, 83)