It was billed as a test for Mark Warburton's Championship leaders who had lost 3-1 to Premiership side St Johnstone in the third-round of the League Cup last September and they certainly had the upper hand against their top-flight opponents.
Gers right-back James Tavernier struck the post with a drive in a first-half and defender Danny Wilson also hit woodwork after the interval.
However, the managerless Ayrshire side - who had player/coach and former Rangers player Lee McCulloch in the dugout as the search for a replacement for Gary Locke goes on - remained disciplined, notwithstanding the folly of substitute Kallum Higginbotham who was shown a straight red card in the final minute for a foul on Tavernier and they will get another chance in the replay at Rugby Park
There was no surprise that Warburton kept the same side with Jordan Thompson and Jason Holt back on the bench as the cup-tied Michael O'Halloran and Billy King made way.
McCulloch made five changes with defender Lee Hodson, on loan from MK Dons and former Carlisle United midfielder Gary Dicker, making their debuts with Stuart Findlay, Steven Smith and Tope Obadeyi also coming in.
There was a sprinkling of chances in a decent but not exhilarating first 45 minutes.
The first came for the visitors in the eighth minute when a fine cross from Greg Kiltie found the head of striker Josh Magennis but his effort slipped past the far post.
A close-range strike from Gers striker Lee Wallace was parried for a corner by Killie keeper Jamie MacDonald, who saved Wilson's rather weak shot following the resultant corner.
In the 18th minute Tavernier rattled MacDonald's left-hand post with a stinging drive from the edge of the box as the home side's grip of the gm took a grip of the match.
There was a weak penalty claim ignored by referee Bobby Madden when wide-man Barrie McKay went down in the box under pressure from Hodson.
Before the break Rangers keeper Wes Foderingham made saves from Obadeyi and Craig Slater as the Rugby Park men reminded the home side of their threat.
Kilmarnock found themselves on the back foot from the start of the second-half and in 57th minute Andy Halliday's 25-yard drive was tipped from the post by MacDonald for a corner which came to nothing.
Harry Forrester and Holt replaced Kenny Miller and Gedion Zelalem respectively as Warburton tried another approach but anxiety grew among the Gers fans as the deadlock remained.
Those nerves frayed further when Tavernier blocked a goal-bound shot from Rory McKenzie on a rare Kilmarnock foray.
Rangers kept probing.
A Wilson header from a Forrester corner hit the crossbar before striker Martyn Waghorn hit the side netting with the rebound.
The Light Blues stepped up the pressure in the closing stages and a great chance was passed up when the unmarked Waghorn failed to control a McKay cross in the box.
In the 89th minute Higginbotham, on for Obadeyi in the 73rd minute, was sent packing for a foul on Tavernier to make it more difficult for the Ayrshire men but they survived to fight another day.