But a tenacious first-half display put Walter Smith’s men on their way to their first victory of 2011 and the visitor’s were brushed aside with surprising ease.
Goals from Lafferty and McCulloch on 20 and 37 minutes meant Rangers were in a commanding position at the break and in the second-half a well-taken penalty from Steven Whittaker put a bit of gloss on the scoreline.
Steven Naismith returned to the starting eleven and the former Rugby Park forward was superb on the left side of midfield this evening.
He was one of three attack-minded players to come into the team which lost the Old Firm derby on January 2, with Lafferty and James Beattie paired up front.
Vladimir Weiss and Richard Foster were both named on the bench alongside Mo Edu with Kenny Miller left out of the squad altogether.
Jamie Ness, meanwhile, kept his place alongside Lee McCulloch in central midfield following a good showing against Celtic.
Rangers had lost just once in their last 36 matches with the Ayrshiremen and they again started positively in this match.
After a minute of play Naismith beat right-back Jamie Hamill with a clever drop of his shoulder but his drilled delivery flew across the six-yard box and out to safety.
And in the next attack Lee McCulloch raking pass found Lafferty but his near post effort went in to the side netting and a goal kick was awarded by referee Stevie O’Reilly.
Despite the pounding rain throughout the first half it was clear that Rangers wanted to make amends for their Old Firm defeat with Naismith and Lafferty, in particular, looking hungry in the early stages.
But the slippery surface was always going to be a test for the sides and on 14 minutes Hamill caught Lee McCulloch with a high boot before Naismith was booked for a bruising challenge on Eremenko in front of the Gers dug-out.
On 19 minutes the opening goal arrived and it was Lee McCulloch that got his first of the season with a wonderful strike.
Lafferty rolled the ball back to the midfielder who bulleted a right-foot shot in to the corner of Bell’s net from 20 yards.
The goal silenced the vociferous Killie fans and Rangers immediately went in search of a second.
Lafferty again used his pace to get down the right wing and Frazer Wright nervously blasted the ball over his own bar.
The home side were clearly in the mood but when Steven Davis was booked, rather harshly, for another strong tackle on Eremenko Ally McCoist could be seen telling his troops to keep their heads in this intriguing Cup battle.
It was not long, however, until Lafferty’s was entered in the ref’s notebook, the big Ulsterman guilty of halting a Killie counter attack having been let off with a late tackle earlier in the game.
With just one goal separating the sides Rangers had to be focused at the back and when Sammon used his impressive pace to sprint clear of David Weir, Allan McGregor was there to palm the striker’s powerful effort away at his near post.
With 36 minutes showing on the Ibrox scoreboards Rangers extended their lead and once again it was a terrific goal, this time by the industrious Lafferty.
The club’s no. 11 again drifted out to the right to collect the ball and as he approached the corner of the 18-yard box he blasted an unstoppable shot across Bell who could do nothing but flap at thin air.
Lafferty thoroughly deserved his fifth goal of the campaign and Smith would have been happy with the resilience his side displayed in a 45 minutes they dominated throughout.
There was to be no changes in personnel for the restart but on 56 minutes Paatelainen decided to make a double substitution with the attack-minded David Silva and Rui Miguel replacing Craig Bryson and holding midfielder Manuel Pascali.
Rangers, however, continued to dominate possession with 19-year-old Ness again putting in an excellent display in the middle of the park.
As the hour mark approached a third goal would have ended this tie as a contest and on 61 minutes it was David Weir that came close to rippling the net.
Davis delivered a teasing corner in to the box and the Ibrox skipper’s downward header bounced off the turf before missing the top corner by a couple of inches.
McCulloch then tried his luck with an ambitious 30-yard rocket which soared in to the Copland Road Stand.
With 23 minutes remaining Walter Smith made a double swap with Weiss and Edu replacing Ness and Beattie.
And it was the Slovakian Weiss that lit up the end of the match with a terrific cameo appearance.
On 71 minutes the tricky winger danced in to the box before being brought down by Hamill and after the ref had pointed to the spot Whittaker stepped up to fire an accurate penalty in to the roof of the net.
With the clock ticking down it was showboat time for Gers and Weiss was denied a goal of the season contender when he darted down the right wing and his right-foot drive was brilliantly saved by Bell.
The ball then fell at the feet of Whittaker on the opposite flank and after cutting inside he looked to find the top corner but again Bell was there to deny the marauding full back.
In the final stages the Killie keeper again did well to tip a McCulloch free-kick over the bar and Jig then had his head in his hands when his instinctive shot from 15 yards cannoned off the post.
For the Rangers fans that travelled to Ibrox tonight they were treated to a fine display from their side who will now return to SPL duty on Saturday when they face Hamilton Accies at Ibrox.