Derek Cornelius gave Gers the lead early in the match, with George Stanger equalising for the visitors before half-time.
Röhl’s men responded in the second-half, with goals from Danilo and Youssef Chermiti securing the three points.
There were four changes from the midweek defeat to SK Brann in the UEFA Europa League as Derek Cornelius, Mohamed Diomande, Bojan Miovski and Danilo all came into the starting line-up.
Oliver Antman was out of the matchday squad through illness, while Nasser Djiga, Joe Rothwell and Youssef Chermiti were named on the bench.
Rangers started with Butland in goal behind a back three of James Tavernier, John Souttar and Derek Cornelius. Jayden Meghoma and Djeidi Gassama were in the wide areas with a midfield of Nico Raskin and Mohamed Diomande. Thelo Aasgaard occupied the number 10 role, with strikers Bojan Miovski and Danilo leading the line.
Ahead of kick-off, the teams were led out by veterans Richard Menzies and Shane Head, with soldiers, sailors and airmen taking to the pitch as part of the club’s annual Remembrance event in tribute to those who have paid the ultimate sacrifice in the line of duty.
It was a strong start to the match from Rangers as they looked to take advantage of an early couple of corners to get a breakthrough in this match. Derek Cornelius saw a header bounce just wide from one of those, as he got on the end of James Tavernier’s delivery.
At the other end, there was a chance for the visitors as Greg Kiltie managed to get a shot away inside the box, but it was straight at Jack Butland and the Rangers number one gathered.
With 15 minutes played, Rangers got their rewards for the strong start as they capitalised on a free-kick opportunity. James Tavernier lifted the ball into a dangerous area, and Derek Cornelius beat the offside trap to get on the end of it and head beyond Edward Beach for his first Rangers goal.
However, the visitors got themselves back level from a set-piece of their own with 38 minutes on the clock. A corner was swung into the box, and Jack Butland was unable to make a connection as he came off his line, with it landing for Stanger at the back post and the defender touched it over the line.
Rangers thought they had restored their advantage just minutes later, but it was ruled offside. Kilmarnock goalkeeper Edward Beach’s goal kick came off the back of Derek Cornelius with Miovski taking advantage and finding the back of the net. However, unfortunately for Gers, the striker was in an offside position, and the teams went in level at half-time.
There was one change at the break for Rangers with Mikey Moore introduced in place of Bojan Miovski.
It was a good start to the second-half for Röhl’s side as Rangers took the lead with 52 minutes played. Jayden Meghoma delivered a fantastic cross into the box from the left, and Danilo got a strong header to send it in off the post for his first Scottish Premiership goal of the campaign.
Bruce Anderson was denied by Butland at the other end as the striker had space to head towards goal, but the goalkeeper did well to tip it behind for a corner.
There were a further two changes for Rangers with just less than half an hour remaining at Ibrox as Max Aarons and Connor Barron were introduced for Mohamed Diomande and Djeidi Gassama.
Röhl made another change in attack shortly after, as goalscorer Danilo was replaced by Youssef Chermiti.
Just minutes after coming on, Chermiti increased Rangers’ advantage with his first goal for the club. The striker was alert as he picked up on a loose pass from Kilmarnock to gain possession at the edge of the box.
It was a good finish as he took a touch onto his right-foot and sent a powerful hit beyond Beach.
A final change saw Lyall Cameron on for the final 10 minutes as he made his first appearance after picking up an injury at the end of August.
Rangers had the ball in the net again shortly after, but Nico Raskin’s strike was disallowed by VAR for offside as the game finished 3-1.
RANGERS: Butland, Tavernier, Souttar, Cornelius, Meghoma, Diomande (Barron, 62), Raskin, Aasgaard (Cameron, 81), Gassama (Aarons, 62), Miovski (Moore, 46), Danilo (Chermiti, 69).
Subs: Kelly, Rothwell, Djiga, Curtis.
Kilmarnock: Beach, Brandon (Williams, 46), Thompson, Mayo (J. Brown, 46), Deas (Brannan, 77), Lyons, Dackers, Kiltie, Watson, Stranger, Anderson (Tiffoney, 68).
Subs: Oluwayemi, McKenzie, J. Brown, Lowery, E. Brown, Polworth