First-half goals from Danny Invincibile and former Heart Gary Wales effectively took the game out of reach of the home side, who did not muster much in the second half.
Hearts were out of the traps quickly and there was an early shout for a penalty after Roman Bednar tumbled in the area under pressure from Graeme Smith, but referee Kenny Clark was not interested.
It was Kilmarnock who took a shock lead after 28 minutes. Steven Pressley slipped at the wrong moment and Steven Naismith waltzed past three defenders, before laying the ball off for Invincibile to fire a shot into the far corner.
Worse was to follow as a slip by Mirsad Beslija ten minutes from the break presented Wales with a shooting chance and a deflection carried his 20-yard shot past Jambos keeper Craig Gordon.
Paul Hartley had a chance to pull a goal back after an hour, but Smith was down quickly to block his effort.
Bednar then slid a left-foot shot wide of target with the Killie defence stretched, but they held on for what proved to be a comfortable victory.