Palace took the lead in the first-half when David Omilabu bundled home a corner, only for us to draw level after the break via an own-goal off defender Sean Grehan.
The visitors re-took the lead via Omilabu from the penalty spot shortly afterwards, but we found an equaliser when Josh Adam smashed home from the edge of the area.
Substitute Alex Robertson looked to have got us the winner when he stroked home a left-footed shot from inside the area, only for Palace's own substitute Ademola Ola-Adebomi to head home deep into added time to ensure the points were shared.
City dominated proceedings early on and could've grabbed a goal in the first minute, but striker Will Dickson couldn't bring the ball under control before it was cleared away.
The visitors found themselves camped in their own half for much of the first period, as we patiently kept possession in search of an opening but the Eagles' defence refused to relent.
Josh Wilson-Esbrand fired in a dangerous ball from the left-hand side that flashed across the face of goal, but Kian Breckin couldn't arrive in time to tap it home.
Adedire Mebude managed to lose his defender after bringing down a long-ball, before setting up Adam to strike, but the midfielder directed his effort straight into the hands of Palace keeper Owen Goodman.
Palace took the lead against the run of play as, in the 33rd minute, a clever corner routine was headed back into the area by defender Grehan, leaving Omilabu to bundle the ball over the line.
We came close to leveling the scores soon afterwards as a clever one-two between Adam and Mebude released the latter to have a shot from a tight angle inside the area, but his effort was palmed away by Goodman, seeing the visitors hold the lead until half-time.
Following the break, we didn't have to wait long to draw level, as a corner from the left-hand side was diverted into his own net by centre-back Grehan in a slice of fortune for the EDS.
But only a couple of minutes later, the visitors were awarded a penalty when Omilabu collided with an onrushing Mikki van Sas, before the Palace winger stepped up to slot the ball home from the spot, restoring their lead.
However, Barry-Murphy's ranks didn't let their heads drop, springing straight onto the attack and were rewarded when Robertson's blocked shot fell to Adam, who smashed the ball beyond Goodman from the edge of the area to level the game once more before the hour mark had struck.
City kept flying forward as we looked to make our momentum count, and, with 65 minutes played, we took the lead for the first time when Robertson fired home a left-footed shot from inside the area to complete the turnaround.
Our defence held firm for 25 minutes and it looked as though we would do enough to secure the win, but in the 94th-minute, Ola-Adebomi lost his marker, rising high to head home a late equaliser and deny us victory.
HOW WE LINED UP
van Sas was given goalkeeping duties against Palace with Ezra Carrington, Finley Burns, Jadel Katongo and Wilson-Esbrand tasked with protecting the Finnish stopper.
Shea Charles captained the side from defensive midfield behind a now familar attacking duo of Kian Breckin and Adam.
Dickson spearheaded the attack as the City no.9 with Mebude and Oscar Bobb providing width in a strong City line-up.
Manchester City Elite Development Squad
Starting XI: van Sas, Carrington (Robertson 46'), Burns, Katongo (Taylor 46'), Wilson-Esbrand, Charles (C), Mebude (Smith 73'), Breckin, Dickson (Sodje 73'), Adam, Bobb
Crystal Palace U21s
Starting XI: Goodman, Imray (Rodney 70'), Adaramola, Ozoh, Grehan, Watson, Omilabu, Wells-Morrison, Akinwale (Ola-Adebomi 70'), Mooney (Cadogan 60'), Gordon.
Substitutes: Shala, Raymond.
WHAT IT MEANS
The draw sees us remain second in the Premier League 2 table, tied on points and goal difference with Crystal Palace.
The EDS hit the road next Saturday, as they travel to Merseyside to take on Everton.
Kick-off at Finch Farm will be at 12:00pm (UK) on Saturday 29 October.
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