3-1 down at half-time, 4-2 down with about 12 minutes to go, Barry Robson's side fought back to produce a stunning win when Michael Dangana netted a late winner in the final few minutes.
The game was played in very difficult conditions at the Hibs training pitch with a strong wind pushing across the pitch. It was certainly not a night for defenders.
The conditions played a part in the opening goal from the home side after about 10 minutes when a free kick from distance caught the wind and deceived Tom Ritchie.
Kevin Hanratty then scored an equaliser after good link up play between the winger and striker Michael Dangana. Hibernian retook the lead from another free kick, this time on the edge of the box. And then they went 3-1 ahead after a defensive mistake inside the area allowed a cut back to be prodded home.
At the other end Aberdeen missed some glorious opportunities to get themselves back into the game before the break. Lewis Duncan did well to create a couple of one on ones but was unable to score, Dangana was unable to force home a Hanratty cross and skipper Connor Barron had a shot which flicked the post.
So some individual errors, and then not taking their chances left Aberdeen with it all to do but the Dons did have the elements behind them in the second half and would still have been confident that they could get back into the game.
And they did just that when Kevin Hanratty scored his second goal of the evening on 55 minutes.
But after more missed chances it was the Edinburgh side would get the next goal and at 4-2 with only 12 minutes to go, the young Dons, who lost their first game of the season last week against Rangers, were heading for a second straight defeat.
But Barry Robson's side have time and time again shown that they are made of stern stuff.
With about ten minutes to go they were given a lifeline when an own goal made it 4-3 after a dangerous Max Barry cross was knocked into the net by a defender.
Then with about five minutes remaining Aberdeen won a corner which saw substitute Kieran Ngwenya win a header and fellow sub Ryan Duncan put it in to equalise at 4-4. Ryan along with all the substitutes came on to help change the game. The Scotland U17 player again impressed.
Aberdeen would not settle for a point and with two minutes to go Michael Dangana managed to find a dramatic late winner.