Motherwell brought in centre-backs Shaun Hutchinson and Tim Clancy following suspension, with Jonathan Page dropping to the bench and teenager Adam Cummins out of the squad.
The first proper attempt on goal in the match didn't arrive until the 25th minute, when Tom Hateley delivered an outswinging corner that Henrik Ojamaa sent goal-bound, but Ben Gordon made the clearance.
Shaun Hutchinson had a header blocked by team-mate Henrik Ojamaa and Gary Harkins opened up the visiting defence to set Dieter van Tornhout free, but Randolph was quickly off his line to make the second touch his.
Moments later, Van Tornhout fired in a shot at the other end that was blocked by Stevie Hammell.
Heffernan powered down on goal and sent in a powerful shot towards the Motherwell goal, but it edged wide.
Immediately after the restart, Paul Heffernan found the opener, taking two attempts to get the ball past Randolph.
Randolph initially made the save from the first attempt, but the ball bounced kindly to Heffernan on the rebound and he knocked it into the back of the net.
The Irish goalkeeper had to work hard to keep out a solid effort from Gary Harkins as the Ayrshire side sought to extend their lead.
With just over an hour played, Hateley handled the ball in his own penalty area and referee Crawford Allan pointed to the spot.
Heffernan stepped up and made no mistake to double his tally for the day.
Moments later, Allan waved away Kilmarnock claims that Hutchinson had handled inside the area again.
Teenage Sub (making his Killie debut) Chris Johnston sent in a shot in the 77th minute that was blocked by Hateley as Kilmarnock continued to press ahead with confidence