Veteran striker Craig Brewster came off the bench to help Aberdeen stay in the Scottish Cup.
Craig Brewster (left) made a huge impact for Aberdeen
Ivan Sproule slammed Hibs in front on 43 minutes when Aberdeen goalkeeper Jamie Langfield failed to hold on to a shot from Steven Whittaker.
But Brewster levelled the game before the hour with a powerful header.
Chris Killen volleyed Hibs ahead again with a wonderful effort but Brewster placed a smart header for Barry Nicholson to lash home a late strike.
The teams will now meet again at Easter Road on Thursday, 18 January, with Gretna awaiting the winners.
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Aberdeen defender Michael Hart replaced the suspended Zander Diamond, while Nicholson, who has recovered from the flu, returned at the expense of Steve Lovell.
Hibs were without the suspended Kevin Thomson, while injuries kept out Scott Brown, Steven Fletcher and Merouane Zemmama.
Dean Shiels was given a start and Whittaker moved into a midfield role, with Kevin McCann making his debut at right-back.
The youngster started the match impressively, as did his similarly callow team-mate Andrew McNeil.
The teenage keeper, making just his third appearance, made a number of good saves early in the game, as both sides committed to attacking strategies.
McNeil gathered a long range free-kick from Scott Severin and stopped a powerful drive from Richard Foster with his knees before the visitors squandered a good opportunity.
Shiels jinked past his marker to the bye-line, but from his cut-back Killen could only make an awkward glancing contact with the ball.
A great pass from Dons midfielder Gary Dempsey allowed Darren Mackie to race through on goal but the striker shot straight at McNeil.
And, when Nicholson followed up with a 20-yard strike, the 19-year-old was at full-stretch to push the ball away.
Ivan Sproule opening the scoring at Pittodrie
Hibs missed another great chance in front of goal, with the sliding Shiels was inches away from connecting with Sproule's low shot.
However, the breakthrough goal came moments later, when Killen did well to recover the ball and feed Whittaker on the edge of the penalty area.
Langfield had Whittaker's shot covered but allowed the ball to squirm from his grasp and Sproule was on hand to find the empty net.
Aberdeen started the second half with Brewster and Chris McGuire on to liven up their forward line.
But Hibs were first to threaten and it needed a good sliding block from Hart to thwart Sproule.
The home side were throwing men forward and were back on level terms after 58 minutes when Mackie scurried down the right flank and crossed for Brewster to thump in a header from 10 yards.
The game grew rather scrappy, with Aberdeen in too much of a hurry and Hibs losing their passing rhythm.
Although, when Hibs did go in front again on 73 minutes, it was a goal of the highest quality.
Michael Stewart sent a searching diagonal pass into the Dons' penalty area and Killen controlled it on his chest before blasting a volley beyond Langfield.
Hibs had failed to beat Aberdeen on their three previous meetings this season and once again fell short, conceding an 88th minute goal.
Severin floated a high ball forward and Brewster was given ample time to nod it into Nicholson's path and the midfielder's shot flew in via the outstretched boot of Rob Jones.
Aberdeen: Langfield, Hart, Anderson, Considine (Brewster 45), Foster, Nicholson, Severin, Dempsey (Maguire 45), Clark, Miller (Lovell 77), Mackie. Subs Not Used: Soutar, Touzani.
Goals: Brewster 58, Nicholson 89. Booked: Severin.
Hibernian: McNeil, McCann (Stevenson 64), Jones, Martis, Murphy, Whittaker, Shiels (Benjelloun 74), Stewart, Beuzelin, Sproule, Killen. Subs Not Used: Simon Brown, Glass, Hogg.
Goals: Sproule 43, Killen 73. Booked: Shiels, Stewart, Benjelloun.
Ref: C Thomson