The sides exchanged chances in the opening ten minutes with Steven McGarry side-footing a shot wide for the home team. At the other end David Lilley sent a header wide from Paul Di Giacomo's corner.
The game erupted into controversy midway through the first period. There appeared to be a nasty stamp by Danny Invincibile on Marc Fitzpatrick that was missed by the referee.
Minutes later Lilley hauled down Clarkson for a penalty as the striker bore down on goal. The defender then appeared to head-butt the forward but was only shown a yellow card.
When the dust finally settled Ross McCormack sent the penalty wide of the right-hand post.
There was little further goalmouth action in the first half, but Motherwell did create the first opening of the second period.
Stephen Craigan's long ball beat the visitors' offside trap but Clarkson's first touch only managed to knock the ball into Alan Combe's arms.
Five minutes later the home side carved Killie open with McCormack's dummy setting up a one-two with Clarkson before he fired the return ball wide of the far post.
The visitors were then reduced to ten men with 20 minutes left when Lilley picked up his second yellow card for a foul on McCormack.
From the on Motherwell were virtually camped in the Kilmarnock penalty area but struggled to find a way through their packed defence.
Even when a Steven Hammell free-kick beat the defensive wall, Combe was on hand to tip the ball over when it looked to be settling in the postage stamp corner.
The Steelmen were not to be denied and, in stoppage time, Clarkson stooped to head home Simon Lappin's cross from eight yards out to secure all three points.