Walter Smith made five changes to the side that beat Celtic three days earlier with a first start handed to Gregg Wylde in midfield.
Sasa Papac and Kyle Lafferty were ruled out by injury and illness respectively, while Steven Davis, Allan McGregor and Kenny Miller were all left out.
That saw Little line up on the right of midfield with Steven Naismith up front, but it was the Northern Ireland man who made the first impact.
In truth Little’s goal was the rare moment of quality in a poor first half, with the breakthrough signalling a flattening of the atmosphere at a half empty Rugby Park.
After a bright opening from the home side that saw Davie Weir booked for a tug on Alexei Eremenko after six minutes it was Rangers who looked more comfortable.
They survived the ball ending up in Neil Alexander’s net from the resulting free kick with Liam Kelly judged to be offside.
It was the only time Alexander was called in to action as the strong looking Rangers backline was well protected by Lee McCulloch and Mo Edu in the heart of the pitch.
That allowed the visitors to control the game to a large degree and Wylde and Little on the flanks were supported by Kirk Broadfoot and Steven Whittaker as they looked to make a way past the home side.
Ultimately it was a simple forward ball from Naismith that set Little free on the right corner of the box, and with few options he lashed the ball past Cammy Bell with a fine strike.
Prior to that moment of magic the sparse crowd were feeding on scraps with the loudest cheer reserved for a collision that saw Madjid Bougherra send Assistant Referee Gary Sweeney tumbling to the turf after a quarter of an hour.
A minute later Weir rose highest to head Wylde’s corner back across goal where Naismith was lurking, but Bell got down well to block.
Killie’s support was growing increasingly frustrated and so were the home players with Conor Sammon and Manuel Pascali joining Weir in the referee’s book before the interval.
The home side clearly responded to whatever message manager Mixu Paatelainen delivered at half time as they came out of the blocks quickly in the second period.
A period of sustained pressure saw Killie force a series of corners including one that called on Alexander to produce a brilliant save to deny Pascali who powered a header just under the bar.
It was a shaky opening five or six minutes for the visitors and Alexander obviously wasn’t happy with how they were defending.
He made his views clear to Bougherra as the pair exchanges some heated words on the edge of the area following a slack moment from the Algerian.
That seemed to be enough to spark the Light Blues back in to life and on the hour mark they got the crucial second through Naismith.
Wylde did well on the left side and when his low driven delivery broke to the Scotland man and he drilled left footed in to the bottom corner.
The home side refused to fold after that goal but it was clear that the visitors had one foot in the semi final.
Walter Smith used the opportunity to make some changes with Naismith and Little making way for Kyle Hutton and Kenny Miller.
Killie responded with two changes of their own but they made little impact on the field as Rangers comfortably saw things out.