Steven Fletcher's injury-time strike gave Hibs a share of the spoils in a thriller at Easter Road.
The Dons opened the scoring just before half-time when Darren Mackie pounced on Rob Jones' error to head home.
They doubled their lead eight minutes after the break when Sone Aluko flighted in a corner and Zander Diamond nodded in from close range.
Jones pulled one back for Hibs with a header in the 62nd minute, before Fletcher sealed an incredible comeback.
Hibs skipper Jones returned to the starting line-up along with Fletcher, while Colin Nish and Joe Keenan were left out.
Aberdeen made only one change from their midweek victory over St Mirren, with Jared Hodgkiss coming in for Charlie Mulgrew.
Lee Miller posed an early threat for the Dons, but Hibs keeper Andrew McNeil managed to gather and Jones replied at the other end with a shot, that was blocked by Diamond.
Derek Riordan missed an opportunity to put Hibs in the lead after 15 minutes when Dean Shiels sent him clear inside the Aberdeen penalty area.
The former Celtic man fired in a left foot shoot, but the ball struck the outside of Jamie Langfield's post.
Langfield was called into action again in the 24th minute, diving to his left to turn Shiels' drive round the post.
Shiels fired in a header from Riordan's corner on the half-hour mark, but the ball sailed harmlessly over the bar.
As half-time approached, Aberdeen capitalised on a Jones blunder when the Hibs captain ducked to allow Andrew McNeil to collect a ball on the six-yard line.
But Mackie sneaked in and headed the ball into the net to give the Dons the lead.
Shortly after the break, Diamond doubled the visitors' tally with a free header from six yards out after Sone Aluko had flighted in a searching corner.
Jones reduced the deficit with 62 minutes on the clock from Riordan's corner. Fletcher struck for the Englishman to nod down from close range and put the home side back in the game.
Scott Severin tried his luck from distance with a powerful drive, but his effort went wide of the target.
With just over 10 minutes left, Fletcher's header was cleared off the line after good work from Alan O'Brien.
Moments later, Riordan powered in a volley that flew just wide of Langfield's post as the home side pushed for an equaliser.
Hibs continued to battle deep into injury-time and their efforts were rewarded when Fletcher tapped in from close range with the final kick of the ball during a goalmouth scramble.
Hibernian: McNeil, Bamba, Hogg, Jones, Murray, Chisholm, Thicot (O'Brien 72), Rankin, Shiels (Nish 80), Riordan, Fletcher. Subs Not Used: Ma-Kalambay, van Zanten, Yantorno, Stevenson, Pinau.
Booked: Jones.
Goals: Jones 62, Fletcher 90.
Aberdeen: Langfield, Considine, Severin, Diamond, Foster, Aluko, Kerr, Young (McDonald 77), Hodgkiss (Mair 72), Miller, Mackie (Maguire 46). Subs Not Used: Bateman, Mulgrew, De Visscher, Stewart.
Goals: Mackie 40, Diamond 53.
Att: 11,640
Ref: S O'Reilly
BBC Sport Player Rater man of the match: Aberdeen's Sone Aluko 8.50 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
Player Rater
~RS~q~RS~~RS~z~RS~35~RS~)