Ross had picked up just one point from their previous nine Scottish Premiership games heading into the derby but they were finally able to celebrate a victory thanks to two first-half goals in quick succession from Scott Boyd and Alex Cooper.
Caley Thistle have now recorded just one win in their last six matches as they find themselves slipping increasingly further away from the top three.
Inverness kept the same starting XI for the match, with the only change coming on the bench where Ben Greenhalgh took the place of Irish youngster Conor Pepper as boss John Hughes looked for his first home win as manager.
Ross made two changes from the side that lost to Aberdeen, with new signing Jordan Slew handed an immediate debut. The on-loan Blackburn Rovers forward took the place of Orhan Mustafi while Gary Glen came in to the side for Dutchman Marc Klok.
Slew was involved in the first chance of the game for County, linking well with Glen, before captain Richard Brittain fired well over Dean Brill's crossbar.
The hosts came closer through in-form striker Billy McKay. Marley Watkins laid off to Doran on the edge of the penalty area and he drilled an effort off the upright, McKay pounced on the rebound but could only turn the ball wide.
County, who last won at Aberdeen on October 5, hit Inverness with a double sucker-punch on the quarter-hour mark to give themselves a two-goal advantage.
First, Slew chested the ball to Glen who nodded into the path of Boyd and the central defender fired into the bottom corner via a deflection from a diving Carl Tremarco.
They then hit the Caley Jags on the break as Slew's ball found Cooper, who held off the attentions of Graeme Shinnie and turned the full-back in the penalty area before angling a left-footed shot beyond Brill's grasp.
An early knock to Watkins forced Hughes to bring on Norwegian Torbjorn Agdestein but it was his strike partner McKay who came closest to scoring next, flicking a Tremarco throw-in straight at Fraser.
The game's first flashpoint came when Steven Saunders appeared to be caught by Danny Williams in a 50-50 challenge right in front of the away dugout. Derek Adams raced from his technical area to pick up the ball and had to be restrained by his assistant Neale Cooper so as to avoid remonstrating with the officials.
Nick Ross planted a header straight at Fraser as Caley Thistle struggled to find a route past the County backline.
Adams' employment of two strikers, Slew and Glen, caused problems for the Inverness defence and made the Staggies look a far more potent proposition.
Graham Carey fired a long-range free-kick over the crossbar at the start of the second period before Fraser parried an effort from Draper. McKay went for the rebound but was beaten to the ball by Brian McLean.
A Doran corner landed on the top of the crossbar and Shinnie floated a cross to the back post that no Caley Jag could get on the end of as the home side struggled to get beyond the County backline.
The day got worse for Inverness and Hughes as Draper was dismissed with 15 minutes to go. He collided in the County half with Stuart Kettlewell and referee Alan Muir deemed that the former Macclesfield man elbowed the Staggies' number four.
Try as they might, Caley Thistle could not find a way through and Agdestein picked the ball up from Williams and drilled an effort over the top of Fraser's crossbar but it was not enough to get the hosts back in the game.
They did get a brief glimmer of hope late on as Doran nodded Polworth's pass over Fraser but it was too late as the Staggies won their first game in Inverness since August 2009.