They didn’t hit the heights they have at times this season but another determined display and a fine second period took them one more step towards the title.
With just ten matches remaining Rangers must find just six victories to ensure a second successive title.
And the manner of victory and the approach to this tricky away fixture suggests they have plenty in their locker that should carry them to the points total they need.
Walter Smith had the opportunity to name an unchanged line up from the team that had seen off the challenge of St Mirren three days earlier.
Madjid Bougherra was again an enforced absentee with a hamstring strain keeping him out of his second successive club match and third game in all.
However despite the early warning offered in that meeting with St Mirren it was again Rangers’ opponents who made the brighter start.
Killie came out fired up and spent the majority of the opening minutes in the Rangers half pressurising a defence that has performed well throughout the SPL season.
The normally composed Wilson, so often a standout when standing in for Bougherra, had a fierce battle with Allan Russell in the early minutes and looked a little ruffled.
The home side did enjoy the better of the first 15 minutes until a crude challenge from Frazer Wright on Miller earned the Killie defender a yellow card and seemed to spark the visitors to life.
Minutes later Steven Davis did well to pick out Boyd wide in the area and he almost set up Wilson for his first Gers goal.
The defender, still in the Killie box after a couple of set piece chances was hunting at the near post for Kris Boyd’s cross but couldn’t get a touch on it.
Boyd has enjoyed a fine record against his old side since leaving Ayrshire for Rangers and he almost added to his tally with a spectacular 19th minute effort from 25 yards.
Collecting a decent pass on the half way line Boyd negotiated a poor surface to loop an effort narrowly off target.
It would have been a fitting way to find his 100th SPL goal for the Light Blues. That wasn’t to be on this occasion but his attempt did signal Rangers becoming more involved in the game.
However they would be grateful for the involvement of their goalkeeper in the 29th minute when Allan McGregor produced a wonderful save to deny Mehdi Taouil.
A decent cross from Iain Flannigan on the left caused confusion between McGregor and his defence but the keeper reacted brilliantly to block Taouil’s effort from 10 yards.
It would prove a crucial stop as it kept his side level at the interval and set them up for a second half display that ensured they will enter a week of cup fixtures with a 13 point lead at the top of the SPL.
A regular feature of the season for Walter Smith’s team has been their improvement in the second period and it took just ten minutes of the second half for them to find the breakthrough.
Just five minutes after Chris Maguire was punished with a yellow card, his defence too were punished when hesitancy allowed Whittaker in.
The full back, a superb influence in the second half, controlled brilliantly and drove beyond Cammy Bell from close range.
It has been something of a habit for Whittaker to score against the Rugby Park side since his arrival at Rangers and he almost added another in the 63rd minute.
Similarly excellent footwork opened up the space, but Whittaker couldn’t find a 12th of the season on that occasion.
However by that stage his side were already two up after a fine striker’s instinct saw Miller fire home from just a few yards after Davis had seen his shot from inside the area saved.
Killie rallied well but couldn’t find a way through the division’s best defence and as Rangers hunted on the counter attack only a couple of slack final passes denied them and addition to the scoreline.
They will not be concerned with that though as they happily travel back up to Glasgow in the knowledge that they can enjoy a break from SPL with a comfortable lead secured.