Aaron Wilbraham gave the Eagles the lead after they had missed a penalty through Ibra Sekajja.
The Magpies' in-form striker Adam Campbell equalised for the visitors, but Sullay KaiKai put Palace ahead once again, only for Orlando Aarons to equalise late in the second period. The first chance of the game fell to Campbell, who latched onto a ball from Dan Gosling, but Lewis Price denied him one-on-one.
Kyle De Silva was fouled in the box after 14 minutes, but Sekajja saw his effort hit the crossbar.
However, they took the lead when Da Silva got to the byeline and fed Wilbraham to find the back of the net from close range.
But it was short-lived as Gosling's effort bounced back into the path of Campbell, who saw a deflected shot go past Price.
Da Silva had others ideas though as he played a good ball into KaiKai, who shot past Magpies custodian Jonathan Mitchell to give them a half-time lead.
Jacob Butterfield came on for Palace at the break and he was soon in the thick of the action by forcing Mitchell to push away an effort from just outside box.
Wilbraham went close with a header while Alex Wynter also went close from a KaiKai corner.
But they were pegged back again on 79 minutes when substitute Aarons found the bottom corner.
U18 star Reise Allassani nearly won it soon after with a curling effort, while the ball was cleared off the line from a Palace corner late on.
And the Eagles survived a late scare when Price took a free-kick which fell into the feet of Campbell, who put the ball into the back of the net, but it was ruled out for offside.