Kris Boyd and on-loan midfielder Jackson Irvine netted to allow manager Allan Johnston to enjoy the winning feeling for the first time since taking the job in the summer.
Killie struck on 17 minutes when Michael Gardyne's header dropped to Boyd, whose initial effort was blocked by Scott Boyd before the striker slid in the knock home the rebound.
Boyd sent a volley over the County bar seven minutes later and Brian McLean scrambled the ball off the line from a Darren Barr header at the back post.
Gardyne send Boyd through with a superb pass just after the break and this time the striker lobbed the ball on to the bar.
County were almost level when a slip from Craig Samson presented defender Mihael Kovacevic with a clear strike but the Killie keeper redeemed himself with an instinctive block.
The home team settled the match when Barry Nicholson rolled the ball square at a free-kick for Irvine to curl home a beautiful strike.