A stunning goal from Tom Rogic in the final minute gave Celtic the win to move four points clear at the top of the table.
The best chances of the game for Celtic fell to Erik Sviatchenko who could only watch as his headed effort went just wide of the far post after 15 minutes and another cleared off the line in the second.
Kilmarnock had chances of their own as Kris Boyd peeled off the back of Charlie Mulgrew at the back post on two occasions.
Craig Gordon positioned himself well to save the first one as the second opportunity just evaded Boyd after it took a deflection.
Celtic had plenty of corners but struggled to create any clear openings with their narrow play and a lack of options out wide.
Kieran Tierney came off injured after 40 minutes and provided the only bright spark in the first half getting to the byline and showed urgency and fight in his play.
Here are the players ratings from today’s game.