Lafferty then volleyed a Steven Davis corner wide of the mark at the front post as the home side put pressure on the visitors' goal.
And the pressure paid off when Lafferty laid the ball off to the onrushing McCulloch at the edge of the box, and the veteran midfielder lashed the ball past the despairing Cammy Bell into the bottom corner of the net.
Immediately afterwards, Lafferty drilled a low cross along the Kilmarnock six-yard box which was deflected by visiting defender Frazer Wright narrowly over his own bar.
Killie
made a rare foray deep into Rangers territory with a
fine run from Alexei Eremenko, who slipped the ball
to Conor Sammon, but the Irishman's shot from a
tight angle was high and off target.
Sammon was presented with the ball again when he dispossessed Rangers captain David Weir, but his shot after a run was parried by Allan McGregor as the visitors tried to force a way back into the game.
However, Lafferty put paid to any hopes Killie had of getting back into things, doubling his side's lead with another right-footed thunderbolt from the angle of the box which left Bell helpless.
Kilmarnock started the second half with a greater sense of urgency and were presented with an opportunity when Jamie Hamill ghosted in behind a ball-watching Steven Naismith inside the Rangers box, but the full back wasted the chance, putting a tame shot wide.
David Weir headed down a Steven Davis corner, but the veteran's effort bounced up and over the bar as the game began to stretch.
Liam Kelly then fired in a speculative 25-yard effort which flew just over McGregor's goal.
But Hamill's clumsy challenge on Rangers substitute Weiss was adjudged worthy of a penalty, and Whittaker stepped up to lash the ball into the roof of the net and seal Rangers' progression to the fifth round.
Sammon was played one-on-one with McGregor as the visitors struggled to find a way to claw back some of the deficit, but the Scotland keeper was equal to the close-range shot
The lively Weiss stung Bell's gloves after going on a mazy run, with Whittaker testing the Killie number one after picking up on the rebound.
Bell again had to look sharp to tip a McCulloch free-kick over as Rangers began to dominate territorially again.
And the midfielder almost netted from the resultant corner, his low shot rebounding off the post.
Silva placed a shot wide of the target with
McGregor rooted to the spot, but the miss summed up
Killie's toothlessness in front of goal as Rangers
finished comfortable winners.
Sandy's Match Pic's are HERE
