County started well and Raith defender Tony Bartholome headed over a John Rankin cross in the third minute. Then the same player booted over an Alex Burke shot a minute later.
The home side continued to dominate, and Steve McGarry set Burke free on the left and the striker's cross was bundled clear by Bartholome. David Winters came close with a curling free-kick that Raith keeper David Berthelot touched round the post.
A goal looked on the cards and a fine delivery from Winters was met by Stuart Taylor, but the former St Johnstone player flashed his header wide.
Raith had a rare attempt at goal in the 28th minute when Paul McMullan flighted a free-kick into the box, but Colin Stewart got up well at the far post to gather the ball.
Bartholome was forced to leave the field seven minutes from the break after going down heavily, and was replaced by under-19 Republic of Ireland international Eamon Fullerton.
County almost broke through in the first minute of the second half when Don Cowie took a quick free-kick, but after a quick one-two with Burke overshot the return and the chance was lost.
At the other end, Raith had a strong claim for a penalty when a Fullerton header appeared to be blocked by Jamie McCunnnie's hands, but referee Ian Brines waved play on.
County brought on Sean Higgins for Winters in the 55th minute in an effort to liven up the attack. They made the breakthrough 12 miutes later when the Raith defence failed to clear their lines and Rankin touched the ball on for Burke to find the net from close range.
Buy Raith still looked dangerous on the break and McMullan played in Clarke, whose shot inside the box was deflected into the side netting.
County should have doubled their lead in the 70th minute when Neil MacDonald whipped in a cross from the left and McGarry just failed to make contact right in front of goal.
County made the points safe in the 86th minute when Higgins swept a Cowie cross in at the far post.