50 Mins
But Killie were a threat on the break and Eremenko, a scorer the last time these sides met in Edinburgh, curved a shot into the arms of Marian Kello.
The hosts were unable to take advantage after Jaakkola spilled a high ball whilst stranded from his line, the ball eventually trickling out for a goal kick.
But the pressure continued from the home side and Templeton had an effort deflected wide before his looping header from Thomson's centre smacked the crossbar and bounced back into the six-yard box before being cleared.
The Rugby Park side should have taken the lead when Kello missed a corner, presenting Manuel Pascali with a chance inside the six-yard box but the Italian's header was wide of the far post.
Killie were enjoying a better spell and Silva cut in from the left and blasted in a shot that spun off a Hearts head and out for a corner.
Thomson dragged a shot wide of the Kilmarnock goal as the first half petered out.
Templeton was prominent at the start of the second half, working his way in from the left and across the edge of the box before getting away a shot that was deflected wide. The Hearts players claimed for a handball but the referee awarded a corner.
And Killie were soon in front as Silva collected the ball near the halfway line and began to drive at the Hearts defence.
The Portuguese forward worked the space to get in a shot from the edge of the box and confidently sidefooted past Kello.
The Ayrshire men were not satisfied with just the one goal and William Gros collected Silva's pass and arrowed an awkward shot towards goal that the crouched Kello blocked with his chest.
But the visitors did get their second when Eremenko received Silva's pass, played a delightful one-two with Gros and finished the move with a shot high into the net.
Hearts were rattled and poured players forward in search of a goal.
But the home side were leaving themselves short at the back and Killie broke with menace on the hour mark.
Eremenko released the speedy Gros on the right but the striker took his shot too early and dragged wide of the far post.
Templeton set up Skacel for a shot on his weaker foot, the right, and Jaakkola was on hand to make the save
Kilmarnock were reduced to 10 men after Eremenko fouled Templeton and then clashed with Zaliukas and the Hearts winger.
Referee Steven McLean issued a straight red card to Eremenko and also booked Zaliukas and Templeton for their part in the shoving match.
Templeton and Thomson flashed shots wide and Jamie Hamill's free-kick for Kilmarnock drifted past Kello's right-hand post.
Jaakkola was called into action in the closing
stages, blocking efforts from Templeton and Adrian
Mrowiec to keep Kilmarnock's clean sheet intact.
Sandy's Match Pic's are HERE
