Iain Vigurs gave the Staggies a first-half lead but a double from Eamonn Brophy and a late header from Nicke Kabamba earned the Rugby Park side the spoils.
It was their first victory in the league since November and ended a run of seven successive defeats.
Kilmarnock made three changes from the team beaten by St Johnstone. In came Laurentiu Branescu, Rory McKenzie, and Brophy for Jan Koprivec, Greg Kiltie, and Harry Bunn.
County also made three changes after their midweek defeat at Ibrox. Richard Foster, Lee Erwin and Oli Shaw made the starting line-up in place of Sean Kelly, Billy McKay and Blair Spittal.
It was the home side who made the brighter start and a move down the left concluded with a Brophy shot that Nathan Baxter did well to save. With the spin on the ball taking it towards the net, Foster intervened with a dramatic clearance.
Kilmarnock then appealed for a penalty when Marcus Fraser bundled McKenzie to the ground but referee Willie Collum was not convinced.
McKenzie was sent flying again in the box 10 minutes later - this time Jordan Tillson was the one challenging - and again the referee insisted it was no penalty.
County were struggling to get into the game but still managed to take the lead after 25 minutes. Josh Mullin's cross was nodded out to Vigurs on the edge of the box, and he had space and time to take a touch before placing a half-volley beyond Branescu.
Despite that setback, Kilmarnock continued to look the brighter of the two sides and they drew level after 54 minutes when Brophy was able to run along the edge of the penalty box before finishing firmly past Baxter.
Just four minutes later and the home side were in front. Coll Donaldson was adjudged to have fouled Chris Burke in the box and this time Collum gave the penalty, which Brophy rolled down the middle as Baxter dived to his right.
Kilmarnock kept pushing to increase their lead and only a brilliant save from Baxter kept out Dario Del Fabro's header.
The home side did get their third, however, seven minutes from time. Burke swung over a free-kick and Kabamba powered a header past the goalkeeper.