Hibernian 0 Kilmarnock 1
He headed in from 16 yards after a long clearance from Alan Combe had dropped between Rob Jones and goalkeeper Andy McNeil.
Hibs had their chances but Combe had an inspired game for Kilmarnock as he protected the three points.
In a tame first half, Steven Naismith cranked it up a bit when he ran from deep inside his own half before unleashing a terrific 25-yard shot which O'Neil tipped over in superb fashion.
Jones kept Combe on his toes with a 29th-minute header from another David Murphy corner but the goalkeeper was well-positioned to block.
Kilmarnock had an amazing let-off three minutes later. Dean Shiels beat the offside trap only to see Combe save his 15-yad shot.
But the ball came off Frazer Wright and struck the post before falling to Shiels again but Combe produced another great stop to keep the scores level.
Steven Whittaker then sliced a shot wide after being set up by Abdessalam Benjelloun.
The only goal came three minutes after the break when Jones misjudged Combe's clearance for Nish to take advantage.
Shiels forced a couple of decent saves from Combe before the Killie goalkeeper produced the save of the match when he clawed away a header from Chris Hogg.
In stoppage time, the goalkeeper excelled again to deny substitute Damon Gray before Steven Fletcher shot carelessly over.