County struck first 10 minutes from the break when Melvin De Leeuw scored with a glancing header from Graham Carey's free-kick.
Bu the Dons kept plugging away and Adam Rooney grabbed an equaliser with a close range finish despite a couple of excellent stops from Mark Brown in the build-up.
Aberdeen mounted the first attack in the second minute when Cammy Smith slipped the ball through to Rooney but County goalkeeper Brown was quick off his line to avert the danger.
The Dons looked up for this one and they created another chance in the fifth minute when Shaleum Logan swung over a ball to the back post for Barry Robson, whose point-blank header was well stopped by Brown.
The County goalkeeper was forced to make another stop from Robson shortly afterwards when the Dons' midfielder drilled in a Rooney cutback.
At the other end Carey swung over a dangerous cross from the left but Mark Reynolds got a touch on the delivery before De Leeuw could pounce.
County thought they had taken the lead in the 21st minute when De Leeuw flicked the ball in for Yoann Arquin, who shrugged off a challenge from Alan Tate and coolly tucked the ball past Jamie Langfield. However, the goal was ruled out for offside.
The home side came close again in the 32nd minute when a De Leeuw effort was blocked on the line by Logan.
But County did take the lead three minutes later when the home side were awarded a free-kick after Andy Considine fouled Erik Cikos. The Dons' defender was booked and when Carey curled in his delivery De Leeuw rose to glance a header into the net.
County were rampant and Arquin was sent clear on goal by De Leeuw - but Langfield raced from his line to block his shot.
Aberdeen made a change at the start of the second of the second half with Joe Shaughnessy replacing Tate.
The visitors looked stronger and after Robson crashed a 30-yard drive off the crossbar a Robson shot at the near post hit Yann Songo'o before going behind for a corner. Robson claimed the County defender had handled but referee Brian Colvin was having none of it.
A Smith header clipped the post and Shaughnessy fired the rebound straight at Brown, before County went on the counter-attack and Carey looked to have been impeded by Considine inside the box - but play was waved on.
It was County's turn to apply the pressure and a poor clearance from Langfield fell to De Leeuw, whose long-range shot was gathered at the second attempt before Arquin could get a touch.
The next goal came at the other end. After a flurry of activity around the County goal which included shots from Jack and Considine, which were saved, Rooney drilled the ball into the corner of the net for his eighth goal in 11 games.
With time running out Carey was through on goal and about to shoot when he was taken down by Considine on the edge of the 18-yard box.
The Aberdeen player was shown a straight red card and Brittain sent his free-kick into the wall and behind.
Deep in injury time Songo'o got on the end of a Brittain free-kick but Langfield made a point-blank save to deny him the winner.