The Buddies made two changes for the match, David van Zanten and Hugh Murray coming in for Aaron Mooy and Marc McAusland who both started on the bench.
And the hosts broke the deadlock just before the half-hour mark when McAusland rose to meet Mooy's corner from the right and power a header past Mark Howard.
Lennon swapped Dargo and McAusland for Wardlaw and Kenneth McLean but they had no time to make any impact before Killie scored their first goal, one that will have left Lennon quivering with rage.