Filip Kiss broke the deadlock four minutes from the break with a superb finish and Richard Brittain doubled the lead after 76 minutes from the penalty spot.
Kris Boyd pulled one back three minutes from the end but County deservedly held out for three vital points.
Michael Gardyne drove at the County defence in the second minute but his shot flew a yard wide of Mark Brown's right hand post.
After a slow start from both sides County finally put pressure on the Killie goal in the 16th minute when a deep cross from Ben Gordon was meant for Jordan Slew - but the big forward just failed to connect.
County had a big shout for a penalty turned down seven minutes later when Slew went on a rampaging run from the half-way line before appearing to be held in the box by Jackson Irvine but referee Kevin Clancy ignored home claims.
The home side were forced to make a change in the 25th minute when Michael Tidser limped off and was replaced by Stuart Kettlewell.
County were on top at this stage and they took the lead in spectacular style four minutes from the break when Kiss swept the ball past Killie keeper Craig Samson from 20 yards after Slew and Melvin De Leeuw combined in the build-up.
Graham Carey came close with a free-kick which curled past Samson's near post, right at the end the first half.
Killie tried hard to get back on level terms and Ross Barber dinked the ball through for substitute William Gros - but his first touch let him down and the chance was lost.
It was end to end stuff now and Manuel Pascali got on the end of a free kick from Sammy Clingan, who had just come on as a sub, but his header flew wide of target.
County pushed for a second and Carey forced Samson to parry his shot in the 70th minute. Brittain nudged the rebound back for Slew - but the ball was intercepted.
The home side doubled their lead six minutes later when Brittain was hauled down in the box by Lee Ashcroft and Kevin Clancy immediately pointed to the spot. Brittain converted the penalty for his seventh goal of the season.
But with just three minutes remaining Killie pulled a goal back when Boyd headed home a deep cross from Jeroen Tesselaar at the back post.
Deep in injury-time Yoann Arquin fired in a shot from just outside the box - but Samson managed to scramble it away for a corner.