Pat Fenlon's side knew they could go top of the SPL - if only for a few hours - with a win at Pittodrie but they got off to the worst possible start when Niall McGinn opened the scoring with only four minutes gone.
However, a stunning equaliser from Irishman Eoin Doyle after 33 minutes ensured the sides went in level at the break. The winner arrived after 70 minutes when substitute Josh Magennis cut the ball back for midfielder Rae to net from close range.
Striker Leigh Griffiths returned to the Hibernian line-up in place of Ross Caldwell. Skipper Russell Anderson, Ryan Jack, Stephen Hughes, Ryan Fraser and Scott Vernon all returned for Aberdeen, with winger Jonny Hayes missing out through injury and Clark Robertson, Chris Clark, Cameron Smith and Magennis dropping to the bench.
The Dons found the back of the net within four minutes when a hopeful ball upfield by Mark Reynolds landed somewhat fortuitously into the path of Vernon and, when his shot was only parried by Ben Williams, McGinn reacted quickest to turn the loose ball home.
The visitors should have equalised after 11 minutes when Paul Cairney fed Griffiths but the striker's effort was well saved by Dons goalkeeper Jamie Langfield.
The Dons could have doubled their advantage after 27 minutes when Ryan Jack picked out Vernon but the Englishman's goalbound effort was blocked by James McPake - with Aberdeen appeals that the Hibs skipper had used an arm to block the header falling on deaf ears.
Hibs got back on level terms with a spectacular equaliser when Doyle controlled a long ball upfield on his chest before producing a stunning strike from 25 yards which fizzed past Langfield.
Alan Maybury, already on a booking, was withdrawn at half-time and replaced by on-loan Manchester City defender Ryan McGivern. The Dons made a change of their own after 55 minutes when Fraser limped off and was replaced by Northern Irishman Magennis.
It was the hosts who were rewarded with a second goal when Magennis used his pace to get by McPake before sending a tantalising ball across goal which was turned home by Rae. Time ran out for Hibernian, who had a late penalty claim when Jack collided with Griffiths turned down, as their six-game unbeaten run in the SPL came to an end.
Source: PA
Source: PA