Nikica Jelavic and Gregg Wylde grabbed the goals on a comfortable night for the Scottish champions.
Kilmarnock surprisingly started the better of the two sides and almost took the lead when Gary Fisher's long range effort had Allan McGreggor scrambling in his goal. But his effort whistled inches past the Rangers post.
Jelavic almost capitalised on a risky back pass to Cammy Bell on 15 minutes, but the Rangers striker failed to get his attempt on target.
Sasa Papac went close for the hosts once again on 21 minutes but the defenders effort did not have Bell worried as the keeper had it covered.
Paul Heffernan caused Rangers problems, the striker showed great pace and movement to break the Rangers defence from a Liam Kelly pass. However McGregor was on hand to beat Heffernan to the ball as the striker looked to latch on to it.
Kilmarnock looked comfortable but as the half wore on, Rangers began to grow and pose more of a threat to their visitors. Jelavic almost gave the home side the lead just before half-time as his downward header was cleared off the line.
Into the second half and Rangers came out showing their intent, with attack after attack.
Steven Davis had the chance from a free kick as Kyle Lafferty was pulled back by Gary Fisher 25 yards from goal. The midfielder struck his free-kick well but the wall did its job and deflected the effort behind for a corner.
On 53 minutes, Juanma Ortiz looked to find Lafferty at the back post with a delicate chip to the back post but Mohamadou Sissoko was on hand to get his head to the ball to deny Lafferty who looked certain to score.
Lafferty did go close however just seven minutes later when the striker found space in the area to get his shot off, but Bell did well in the visitors goal to deny the Northern Ireland international.
On 64 minutes came the breakthrough when a free-kick on the edge of the area from Steven Davis was pulled back to Jelavic who had dropped off. The striker made no mistake, side footing his effort into the corner giving the impressive Bell no chance.
And just two minutes later Rangers doubled their lead with a superb counter attack. Gary Harkins thundered his header against the Rangers bar from a corner. Edu picked up the ball and looked to counter Kilmarnock as the midfielder showed terrific pace to get into a position to square the ball to Wylde who made no mistake, tapping in from 12 yards.
Rangers never looked in danger from there on in. They could have added a third but Davis had his effort saved by Bell after a neat one two with Jelavic.
Rangers dominated the remainder of the game but could have conceded when Liam Kelly's long range effort fell just wide of the Rangers goal.