Ross McCausland and Abdallah Sima had Rangers 2-0 ahead at the break before Kilmarnock got one back through a Daniel Armstrong penalty, but the Light Blues responded quickly with Todd Cantwell restoring the two-goal advantage at Ibrox.
Philippe Clement named two changes to his side from Saturday’s Old Firm derby as John Souttar came in for the suspended Leon Balogun, with Kieran Dowell also starting the match and Dujon Sterling on the bench.
That meant Rangers lined-up with Jack Butland in goal and a back four of James Tavernier, Connor Goldson, John Souttar and Ridvan.
Dowell came into midfield alongside John Lundstram and Todd Cantwell, while Clement stuck with the same front three of Abdallah Sima, Cyriel Dessers and Ross McCausland.
There was a place on the bench for new signing Fabio Silva, while Nico Raskin was named in the matchday squad for the first time since October 29 as he makes his return from injury.
They were joined on the bench by Robby McCrorie, Sam Lammers, Rabbi Matondo, Dujon Sterling, Scott Wright, Leon King and Adam Devine.
Clement said pre-match he was looking for energy from his side and he got that in the opening stages as they searched for an early breakthrough at Ibrox. Cantwell drove deep into the Kilmanock half before feeding the ball out to Abdallah Sima on the left. The on-loan Brighton winger sent a ball into the box in search of Cyriel Dessers but the visitors were able to clear the early danger.
In another attack, Kieran Dowell picked up on a loose pass from Joe Wright to combine with Ross McCausland. The ball was sent towards Dessers in the box but his strike was just wide of the target.
Kilmarnock had a shot over the bar from Corrie Ndaba after a free-kick was whipped into the box by Matthew Kennedy but it failed to trouble Rangers number one Jack Butland.
William Dennis was forced into a good save with 16 minutes on the clock as Connor Goldson picked out Abdallah Sima with a lovely cross ball and he was able to get a strong low drilled effort at goal but Dennis got down quickly to his right to tip the ball out for a corner.
Dessers came close to a breakthrough shortly after as he got his head on the end of a great delivery from Ridvan but it was just high of the target from the striker.
At the other end, Butland pulled off a superb stop to deny Kilmarnock the opening goal as David Watson sent a ball forward into the path of Kyle Vassell to send him through one on one with the Rangers goalkeeper. The striker released a right-footed effort at goal but Butland was out quick to block the shot and keep the score level.
WIth five minutes to go in the first half, Rangers had the breakthrough and it was a first Scottish Premiership goal for Ross McCausland.
The move started at the back with Ridvan and Sima combining on the left inside the Rangers half. With Kilmarnock attempting to put some pressure on before half-time Clement’s men broke as Sima found Dessers just inside the Kilmarnock half.
The striker did well to spot the run of McCausland as he lifted the ball into the path of the youngster who had beaten David Watson for pace and showed composure to finish low into the back of the net.
Just a few minutes later, Rangers doubled their advantage at Ibrox. Connor Goldson sent a ball into the box with Abdallah Sima taking a touch to send the ball in the air, before striking an unstoppable shot beyond Dennis.
Into the second-half, there was a VAR check for a handball as Rory McKenzie’s cross came off John Souttar’s arm as he tried to block the delivery into the box. John Beaton was called over to the screen, and after a review he pointed to the spot and awarded the visitors a penalty.
Daniel Armstrong stepped up and got one back with a left-footed finish low into the bottom corner.
However, it wasn’t long until the two goal advantage was restored at Ibrox as Sima and Ridvan again combined down the left to create an opening for Rangers. It was Ridvan who provided the assist with another good delivery into the box with Todd Cantwell on hand to tap home from close range.
With 20 minutes remaining at Ibrox, Clement turned to his bench for the first time in the match as Fabio Silva was introduced for his Rangers debut, alongside Dujon Sterling.
There was another great chance for Gers to increase their tally as Ross McCausland released Todd Cantwell through on goal, but Dennis was able to come out and block the shot to send it out for a Rangers corner.
For the final period of this match, Scott Wright and Rabbi Matondo were introduced in place of Abdallah Sima and Ross McCausland.
Raskin made his return from injury for the final few minutes in the match as he replaced Todd Cantwell.
It was another important three points for Clement’s men as they head into the winter break, which will include a training camp in Spain.
RANGERS: Butland, Tavernier, Goldson, Souttar, Ridvan, Lundstram, Dowell (Sterling, 70), Cantwell (Raskin, 89), Sima (Wright, 83), McCausland (Matondo, 83), Dessers (Silva, 70).
Subs: McCrorie, Lammers, King, Devine.
Kilmarnock: Dennis, Ndaba (Deas, 86), Wright, Mao, McKenzie, Vassell (Watkins, 62) , Kennedy, Armstrong (MacKay-Steven, 62), Findlay, Donnelly (Watson, 18), Polworth.
Subs: O’Hara, Sanders, Murray, Davies, Dallas.