Kilmarnock 0 Hamilton Academical 1
Richard Offiong's controversial strike sent Billy Reid's men nine points clear of bottom club Inverness.
Killie appeared to be suffering from a Scottish Cup hangover in a sluggish first half.
In fact, if goalkeeper Alan Combe had been as lethargic as his team-mates, Accies would have had the game won at the interval.
The keeper made two excellent saves midway through the first period - the first after Hamilton's central defender Mark McLaughlin had shown good feet on the edge of the box and fired a shot towards the far corner which Combe did brilliantly to tip around the post.
More Kilmarnock defensive dithering gave Hamilton their best chance of the half when James Fowler hit a pass to Simon Ford and left James McCarthy and Offiong clear.
McCarthy released the striker who tried to chip the keeper, but Combe pawed it away straight to McCarthy who prodded the ball against the post with the outside of his right foot when it looked easier to score with his left.
It was level at the break but Accies were ahead within a minute of the restart with a disputed strike.
Hapless referee Craig Thomson had seen fit to issue five yellow cards in a first half that was never dirty and continued his error-strewn afternoon by awarding a corner to Hamilton when the ball had clearly come off an attacker.
Paul McGowan made the most of the gift, sending over a wicked ball which Offiong did well to head low into the corner of the net despite Garry Hay's best efforts to clear.
McGowan almost made it two soon after but Combe made another good stop to block his well hit volley.
Kilmarnock's first shot at goal came in the 68th minute when Danny Invincibile's 20-yard effort flew narrowly past, but it was Hamilton who remained in total control.
Killie boss Jim Jefferies recently rated his side's performance at Easter Road as one of the finest of his tenure at Rugby Park, but this must have been one of the poorest.