County substitute Liam Boyce pulled one back with nine minutes left on the clock but Killie held on for all three points.
County started on the front foot and Yoann Arquin tested Killie's Craig Samson in the first minute with a rasping drive but the keeper got a finger tip to the ball.
Graham Carey was looking lively early on he left a couple of defenders for dead on the left but his cross into the box was poor.
The County fans showed their appreciation for departing fans favourite Stuart Kettlewell after four minutes with a round of applause.
County won a free kick in a dangerous position and Carey's effort stung the gloves of Samson but the keeper recovered to smother the ball.
Killie were seldom seen as an attacking force in the early stages but Ross Barbour shipped in an inviting ball into the danger area in the 17th minute but there were no takers.
Carey was prominent in County's forays in the final third and after playing a neat one-two with Uros Celcer his across the six yard line was just missed by De Leeuw.
The County wide man threatened again just before the half hour mark when he cut inside and let fly with his right foot but Samson saved comfortably.
Killie started to push forward towards the end of the half and a good run and cross by Obadeyi was scrambled away.
The visitors came close again seconds later when Mark Connolly got on the end of a Craig Slater free-kick but his header on the six yard line was well saved by Antonio Reguero.
But Slater's next delivery into the box proved fatal for County. Magennis rose highest and nodded past Reguero for the opener.
County had a great chance to level right at the start of the second half. Jordi Balk sent over a superb ball for Jervis but the big forward miss-controlled the ball at the vital moment and Samson gratefully pounced on the loose ball.
But it was Killie who doubled their lead in the 56th minute when Ross Barbour sent over an innocuous looking cross and the County defence parted as Obadeyi headed into the corner of the net.
County immediately made a double substitution with Joe Cardle and Richard Brittain coming on for Filip Kiss and Arquin.
The home side kept pushing to get back into the match and Carey made a darting run into the box only to be denied by a last ditch tackle by Magennis.
But County were thrown a lifeline in the 81st minute when substitute Boyce got on the end of a deep cross from Cardle to head in from close range.
But despite a late flurry of activity towards the Killie goal the visitors held out for their first win of the campaign.