There was little danger when Craig Bryson's ambitious 20-yard volley bounced in front of Fraser, but the keeper lost concentration and the ball jumped out of his grasp, hit the post and fell perfectly for Aime Koudou who had the simple task of scoring his first Killie goal.
Not to be out-done, Kilmarnock gifted the visitors a leveller in the 22nd minute.
Fraser Wright skied a clearance at the edge of his box. Alan Combe came charging out to claim it, but Simon Ford heard nothing as he calmly nodded the ball down and watched in horror as it trundled into his own net.
Home skipper David Lilley could have put his side ahead within two minutes when Fraser flapped at a corner, but he blazed over form six yards.
Killie had another chance on the half-hour mark when a sweeping move ended with Bryson side-stepping the last defender, but this time Fraser saved well with his legs.
Combe had to produce a brilliant diving save to keep his side level two minutes after half-time as he repelled Marius Niculae's powerful header.
And the Killie keeper was instrumental in his side's second goal. His long clearance was missed by the Caley defence and Colin Nish judged the bounce perfectly and jumped bravely to beat Fraser to the ball before heading home.
The lead lasted just five minutes though as Lilley fouled Roy McBain 25 yards out giving Don Cowie the opportunity to send a fierce free-kick sailing high into the far corner.
Chances were few and far between in the final stages, but substitute Ryan Jarvis looked to have been given a golden opportunity with five minutes left when Nish's angled cross seemed perfect for him, but he was caught flat-footed and the point-blank chance was gone.
Caley had the chance to win it in the last minute after nifty footwork from Cowie saw him reach the byline and pick out Graham Bayne, but he placed his shot just wide.