The Dons had the best of a poor first half with Adam Rooney going close.
Derek McInnes' side bossed the second period, and the crucial goal arrived when Quinn diverted into his own net from Shay Logan's delivery.
The win takes Aberdeen up to fifth in the table and they are now just three points off top spot.
A victory would have taken County above Motherwell but the Highlanders remain in bottom spot with five points from their 12 outings.
The game started in driving rain and Dons defender Mark Reynolds made an unorthodox acrobatic clearance in front of his own goal in the opening seconds, with Yoann Arquin waiting to pounce on Graham Carey's deep cross.
At the other end Adam Rooney drew a decent save from Staggies keeper Mark Brown with a near-post header from Logan's centre.
And Brown was called into action again when Niall McGinn's floated free-kick picked out Ash Taylor at the back post. His header back across goal took a touch off County defender Scott Boyd but Brown reacted well to palm the ball away.
On a rare foray into the visitors' box, County's Quinn rose brilliantly but nodded just wide of keeper Scott Brown's right-hand post from Michael Gardyne's excellent delivery.
Rooney flashed a header narrowly wide from McGinn's cross late in the half and the sides went in all square at the break, no doubt delighted to escape the deluge in Dingwall for 15 minutes.
County looked sharper at the start of the second period with Gardyne the main architect of their good play going forward.
They still had to be alert at the back though and Darren Barr brilliantly headed clear from under his own bar after Jonny Hayes broke down the left and whipped a great ball into the box.
Minutes later the home side fell behind in calamitous fashion. Boyd's poor pass was pounced on by McGinn, who raced down the right and sent a ball into the box that Quinn fired into his own net from a few yards out.
Andrew Considine fired over the bar from 12 yards as Aberdeen chased a quickfire second, and the excellent Hayes continued to cause County problems down the left during a period of intense Dons pressure.
The second almost came following a superb move. Logan drove a ball into the area and Peter Pawlett took a glorious first touch to escape the attentions of Boyd, but his right-footed shot crashed off the angle of bar and post.
And the hosts almost cashed in on that piece of good fortune when Carey's dig from distance was palmed out by Brown, but substitute Liam Boyce could only lash the rebound well over the bar.
That was as close as the Staggies came to a leveller and the visitors could have increased their lead as Hayes and Willo Flood passed up good chances, but Quinn's horror moment was enough to secure the Dons' first competitive win over County in Dingwall.
Match ends, Ross County 0, Aberdeen 1.
Second Half ends, Ross County 0, Aberdeen 1.
Attempt missed. Willo Flood (Aberdeen) right footed shot from the centre of the box is too high.
Jeffrey Monakana (Aberdeen) is shown the yellow card.
Foul by Jeffrey Monakana (Aberdeen).
Lewis Toshney (Ross County) wins a free kick on the left wing.
Attempt blocked. Graham Carey (Ross County) right footed shot from outside the box is blocked.
Foul by Ash Taylor (Aberdeen).
Jake Jervis (Ross County) wins a free kick in the attacking half.
Substitution, Aberdeen. Jeffrey Monakana replaces Jonny Hayes.
Attempt saved. Willo Flood (Aberdeen) right footed shot from long range on the left is saved in the top right corner.
Attempt missed. Niall McGinn (Aberdeen) right footed shot from outside the box is too high.
Foul by David Goodwillie (Aberdeen).
Scott Boyd (Ross County) wins a free kick in the attacking half.
Substitution, Aberdeen. Barry Robson replaces Peter Pawlett.
Corner,  Aberdeen. Conceded by Scott Boyd.
Niall McGinn (Aberdeen) wins a free kick in the defensive half.
Foul by Darren Barr (Ross County).
Foul by Mark Reynolds (Aberdeen).
Lewis Toshney (Ross County) wins a free kick in the attacking half.
Substitution, Aberdeen. David Goodwillie replaces Adam Rooney.
Attempt saved. Jake Jervis (Ross County) right footed shot from the centre of the box is saved in the centre of the goal.
Attempt blocked. Willo Flood (Aberdeen) right footed shot from outside the box is blocked.
Attempt blocked. Jonny Hayes (Aberdeen) right footed shot from outside the box is blocked.
Attempt saved. Ryan Jack (Aberdeen) header from the centre of the box is saved in the centre of the goal.
Foul by Peter Pawlett (Aberdeen).
Filip Kiss (Ross County) wins a free kick in the defensive half.
Corner,  Aberdeen. Conceded by Graham Carey.
Attempt missed. Peter Pawlett (Aberdeen) right footed shot from the centre of the box is too high.
Attempt missed. Graham Carey (Ross County) right footed shot from outside the box is close, but misses to the left.
Foul by Andrew Considine (Aberdeen).
Darren Barr (Ross County) wins a free kick in the attacking half.
Corner,  Aberdeen. Conceded by Scott Boyd.
Attempt missed. Liam Boyce (Ross County) right footed shot from the centre of the box is too high.
Attempt saved. Graham Carey (Ross County) right footed shot from outside the box is saved in the centre of the goal.
Substitution, Ross County. Liam Boyce replaces Michael Gardyne.
Peter Pawlett (Aberdeen) hits the bar with a right footed shot from the centre of the box.
Michael Gardyne (Ross County) is shown the yellow card.
Jonny Hayes (Aberdeen) wins a free kick in the attacking half.
Foul by Michael Gardyne (Ross County).
Paul Quinn's own goal gave Aberdeen victory over Ross County, who missed the chance to move off the foot of the Premiership table.