The hosts have battled back from 3-0 down after having more than their fair share of the first-half chances.
Samaras turned goalscorer five minutes later, finding space in the box and firing the ball into the top corner. He doubled his tally straight away, playing a neat one-two after being gifted the ball and placing a low shot beyond the goalkeeper.
Killie did give themselves a lifeline with 10 minutes to go. Michael Gardyne was brought down on the edge of the Celtic box and Sammy Clingan stepped up to curl an excellent free kick into the top corner.
Clohessy then got his side right back into the game, taking advantage of poor defending from Emilio Izaguirre and putting the ball beyond the goalkeeper just before half time.