Behind 1-0 at the break, it was a fantastic response from Röhl’s men as a double from Youssef Chermiti and a Mikey Moore strike sealed the points.
From the midweek victory over St Mirren there were two changes as Dujon Sterling and Connor Barron both came in from the start, with captain James Tavernier and Mohamed Diomande on the bench this afternoon.
That meant Rangers started with Jack Butland in goal behind a back four of Dujon Sterling, John Souttar, Emmanuel Fernanadez and Jayden Meghoma.
Barron joined Nico Raskin in midfield, while Thelo Aasgaard, who has scored in the last two fixtures, adopted the more advanced role in the middle of the pitch. Youssef Chermiti led the line this afternoon, with support from Djeidi Gassama and Mikey Moore.
There was also a boost on the bench as striker Bojan Miovski returned from illness to make the matchday squad.
It was John Souttar who had the armband this afternoon, as he led the team out for the second Old Firm derby of the Scottish Premiership season.
Rangers got the action underway, and the first 10 minutes were fairly even in what was a huge fixture for both sides. McCowan drilled a low strike wide for the hosts, before a corner saw them threaten again as Auston Trusty sent a header wide from Engels’ corner.
Jack Butland pulled off a superb save to deny Johnny Kenny as the Rangers number one got his body in the way of a close-range strike.
However, just seconds later, Celtic had the advantage. A throw-in saw Hyunjun Yang play a one-two and drive towards the Rangers goal, before blasting a right-footed strike high into the back of the net.
At the other end, there was almost a response through Gassama, but Schmeichel did just enough to get a touch to send it behind for a corner.
There was another big save from Butland as he got down low to his right to push away another strike from Kenny, before Fernandez had to follow up on the line to hook away a header from the home side. In first-half injury time, Rangers had the ball in the back of the net, as Moore touched home a Youssef Chermiti cross but the linesman's flag was up for offside to send the teams in level at the break.
Röhl made one change at half time as he introduced Mohamed Diomande in place of Thelo Aasgaard for the second half.
It was the perfect start to the second-half as Rangers got level in just five minutes. A throw-in was played to Nico Raskin, and he skipped towards the byline before cutting back to Chermiti in the box. It was a composed finish from the striker from close range as the squad ran off to celebrate in front of the away supporters.
Butland was again on hand to deny the hosts with a crucial block on a strike from Maeda, before Barron saw a shot deflected wide at the other end.
With an hour played, Rangers had the lead for the first time in the match, and it was another for number nine Youssef Chermiti. The striker picked the ball up on the left flank and drove towards goal before getting a right-footed shot away. It took a nick off the foot of Schmeichel, but it wasn’t enough to deny the Portuguese forward a double.
It was a superb second half from Gers and Röhl’s men extended their lead with Mikey Moore finding his third goal of the season. Gassama fed a perfectly weighted pass into the path of the on-loan Spurs winger and he finished beyond Schmeichel.
Captain James Tavernier was introduced for the final period as he replaced Djeidi Gassama, before Miovski came on for double goalscorer Chermiti as the game entered extra time.
Rangers saw out the five minutes of added time for victory in the second Old Firm derby of the league season.
RANGERS: Butland, Sterling, Souttar, Fernandez, Meghoma, Barron, Raskin, Aasgaard (Diomande, 46), Gassama (Tavernier, 86), Moore, Chermiti (Miovski, 90).
Subs: Kelly, Nsiala, Aarons, Curtis, Dowell, Diomande, Danilo.
Celtic: Schmeichel, Trusty, Nygren (Hatate, 73), Yang, McCowan (Araujo, 68), Kenny (Yamada, 73), Engels, Maeda, McGregor, Ralston (Forrest, 87), Tierney (Scales, 87).
Subs: Sinisalo, Bernardo, Murray, Donovan.