The game was only 90 seconds old when on-loan striker Andy Walker tapped in a Tony Rougier pass to give him and his team a dream start.
With half time approaching, the Dons equalised through Billy Dodds, who latched on to a David Rowson ball to shoot past Chris Reid.
In the 68th minute, birthday boy Eoin Jess made it 2-1 for the Dons with a 20 yard strike.
That looked like it would seal the three points for Aberdeen until Walker made it two apiece with just six minutes remaining, heading home a Tony Rougier cross.