In a pulsating match the visitors got off to a flyer with Faissal El Bakhtaoui netting after just four minutes.
Neil McCann’s men saw out the first-half with ease as they looked to be in control.
However, they took their foot off the gas in the second 45 to allow the hosts back into the game.
Just after the hour Gordon Greer smashed home Killie’s equaliser after Kris Boyd knocked down a Jordan Jones corner.
