With a question mark hanging over his future, Miller was left out of the squad for the clash at Ibrox, the Scottish champions having already accepted an offer from Birmingham and the player reportedly also in talks with Fiorentina.
The 22-goal striker netted a hat-trick the last time the two sides met but this time the goals were shared among Lee McCulloch, Kyle Lafferty and Steven Whittaker.
Miller was the most notable omission from the line-up tonight as Walter Smith made three changes from the side who lost the Old Firm derby. Lafferty, James Beattie and Steven Naismith were all drafted into the team, with Richard Foster and Vladimir Weiss both dropping to the bench.
Manuel Pascali and Garry Hay both started for Killie in place of James Fowler and Ben Gordon, who returned to Chelsea following the end of his loan spell.
Kilmarnock’s recent impressive form meant a shock could have been on the cards and Rangers set about trying to stamp their authority on the tie early on.
McCulloch picked out Lafferty at the back post and the big striker had a decent chance to open the scoring but sent his angled drive fizzing past the post.
He had another opportunity moments later, this time connecting with Steven Davis’ corner, but again he was off-target with the shot.
The breakthrough came after 20 minutes when Davis embarked on a run into the box before trying to set up Lafferty. He connected awkwardly and cut back for McCulloch instead, who sent a firm low shot into the back of the net from 25 yards.
At the other end, Killie were threatening when Mehdi Taouil slipped a neat pass to Alexei Eremenko and he teed up the shot for Conor Sammon – but he failed to add to his 15 goals this season in blasting well over.
The visitors then carved out another chance when David Weir lost possession to Sammon and he tested Allan McGregor with a point-blank shot but the goalkeeper was up to the challenge.
Rangers doubled their advantage with 37 minutes gone when Sasa Papac picked out Lafferty on the right flank with a lovely pass and, with no support, he had a go from distance and did well to drill past Cammy Bell in the Killie goal.
Kilmarnock were forced to make a change with just under an hour gone when skipper Craig Bryson limped off to be replaced by David Silva. Pascali also made way for Rui Miguel.
Maurice Edu then made his return after several weeks on the sidelines through injury when he replaced youngster Jamie Ness after 67 minutes, while Beattie was withdrawn for Weiss as the home side also made a double switch.
Weiss had an almost immediate impact on the game when he was tripped in the box by Jamie Hamill, with referee Stevie O’Reilly pointing to the penalty spot and showing a yellow card to the Kilmarnock player.
In the absence of Miller, Whittaker stepped up for the spot-kick and confidently lashed high into the net to put the tie beyond Mixu Paatelainen’s men with 71 minutes on the clock.
Rangers were still hungry for goals and Weiss weaved his way into the box before forcing a superb save from Bell, who then did well to block McCulloch’s free-kick from the edge of the box.
Substitute Richard Foster saw his low drive crash off the post in the final minutes but, by then, Rangers were assured of their place in tomorrow’s draw at Hampden anyway.