Quinn picked up a ball from Stuart Kettlewell and struck the ball from range to secure all three points for the home side.
The away side made a promising start to the game dominating early possession but they found it difficult to break down a resilient Ross County defence.
Chances were at a premium in a disappointing opening half and the first shot in anger was fired in after 10 minutes by Aberdeen's Jonathan Hayes whose right-footed effort was blocked.
Ross County tried hard to establish themselves but their only shot of the half came from Rocco Quinn whose effort from distance went high and wide
Niall McGinn then went close for Aberdeen in the 27th minute but his long-range effort was wide of Mark Brown's right-hand post.
The game began to liven up as the half was coming to a close. First Quinn fired wide for the home side before McGinn mustered the only shot on target for either side in the half with a long-range effort that was comfortably saved by Brown.
County began the second half with intent. Steven Ross fired wide in the early stages before the home side stunned Aberdeen by taking the lead in the 52nd minute.
Kettlewell played the ball Quinn who crisply struck the ball home into the top left corner from outside the area.
Aberdeen tried to bounce back but Scott Vernon's header just shy of the hour mark failed to cause Brown any problems.
County nearly extended their lead moments later but Graham Carey's shot from an acute angle was saved by Aberdeen goalkeeper Jamie Langfield.
The contest began to open up with both sides forcing corners as the second half wore on, but it was County who looked the more threatening
Carey forced Langfield into a save before Ross and Kevin Luckassen both had efforts that missed the target.
Aberdeen forced five corners in succession as the game drew to a close but Ross County defended valiantly.
Michael Hector thought he had snatched a point for the away side but his effort from distance was plucked away by Brown ensuring Aberdeen slipped to their first defeat in seven matches.