Scorers: Kilmarnock: Fowler (2)
But Killie got off to a flyer with an early goal.
Jereon Tesselaar swung a cross in from the left and Rory McKenzie’s lay-off was swept high into the net by Fowler.
The visitors had another chance in the sixth minute when they were awarded a free-kick just outside the 18-yard box. But James Dayton’s effort flew narrowly over the crossbar.
Killie were almost in again when Michael Fraser made a hash of a clearance. Dayton picked the ball up on the edge of the area but he was crowded out.
At the other end, Martin Scott did well to get the ball into the danger area and Sam Morrow’s knock down was flashed past the upright by Richard Brittain.
County continued to press and there were claims for handball in the Killie box from Scott Boyd’s downward header following a Paul Lawson corner.
It took a brilliant full length save from Cammy Bell to keep a low drive from Brittain going in at the left-hand post, with the Killie goalkeeper required some treatment before he was able to continue.
County were going all out for a leveller and Iain Vigurs fired into the side netting in the 31st minute as the home side continued to turn the screw.
It was practically one-way traffic and a long ball from Brittain fell for Boyd, who blasted well over from 15 yards.
Dayton was forced off after an accidental clash with Mihael Kovacevic and Cillian Sheridan replaced him as Killie reshuffled the pack.
In first-half stoppage time, Brittain was slipped through by Vigurs but his effort was blocked in front of goal.
County created the first opening of the second half in the 55th minute when Kovacevic crossed the ball for Brittain, whose back flick let in Morrow but his shot was easily saved by Bell.
Kovacevic was causing a lot of problems down the right and his cut back set up Brittain with a chance but his shot was blocked en route to goal.
Killie had a chance to apply pressure on the County goal when they were awarded a free kick 25 yards out but Sheridan blasted his shot well wide of the left-hand post.
County were starting to turn the screw and Morrow was desperately unlucky with a low shot which beat Bell but rebounded off the near post.
The home side made a double substitution in the 72nd minute, with Gary Glen and Steven Ross coming on for Lawson and Scott.
Despite County’s dominance Killie should have wrapped it up in the 86th minute when Sheridan raced on to a McKenzie pass but the former Celtic forward fired well off target.
But most of the action was at the other end and Bell made a stunning save in injury time when he denied Steffen Wohlfarth in the 92nd minute.
County had another chance to grab an equaliser in the last attack of the match but Evangelos Ikonomou scuffed his shot wide of the far post.