Lithuanian debutant Deividas Cesnauskis capped a fine display with the third early in the second half to kill off the lightweight Ayrshire side.
And it could have been even worse as the Jambos passed up another two chances in a devastating opening spell. Stephen Simmons should have scored in the third minute but fired his shot wide from eight yards.
The Killie defence didn't heed the early warning and were posted missing as 17 year-old left-back Lee Wallace ran unopposed from his own half to combine with Dennis Wyness inside the box and show remarkable composure to lift the ball over Alan Combe for a sixth minute opener.
Hearts went two ahead in the 13th minute thanks to Lee Miller's opportunism. Paul Hartley's free-kick skimmed off Simon Ford's head, but Miller reacted quickly and powered a header in at the far post.
Hartley had the chance to kill the game two minutes later when Simmons sent him clear for a breakaway. The midfielder was poised to slide the ball past Combe when David Lilley risked all to pull off a superb sliding tackle to rescue the situation.
Anything less than perfection would have led to a red card for Lilley and a penalty to Hearts.
Surprisingly Hearts had to wait until the second half for the third goal when debutant Cesnauskis fired into the roof of the net after good work from his countryman Saulius Mikoliunas.
Kris Boyd's last-minute goal from the penalty spot after Wallace's foul on Allan Johnston was scant consolation for Killie.