A tumultuous week had a happy ending for Rangers. The manager has changed, so too did their fortunes.

The Scottish Cup meeting with Morton had been seen as a make-or-break encounter for Mark Warburton but it was always going to be more important for Rangers. In the end, the Englishman never made it this far.

But the players that he left behind at Ibrox got the job done as they progressed to the quarter-finals and a tie with Dunfermline or Hamilton Accies. Only time will tell who will be in the dugout come then.

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The only certainty is that it won’t be Warburton. The departure of the 54-year-old, assistant manager David Weir and Frank McParland, the Head of Recruitment, on Friday evening ensured this was never going to be a straightforward afternoon at Ibrox.

Come the end of the 90 minutes, goals from Kenny Miller and Martyn Waghorn had won it for Rangers. It was a result greeted with relief as much as celebration.

Having been thrown into the spotlight, Graeme Murty now has a chance to reflect on a whirlwind weekend. He will take charge of training at Auchenhowie in the coming days, but there is no guarantee he will be in the dugout at Dens Park on Sunday.

Rangers’ preparations for the Ton test may have been disrupted by the departure of Warburton but most of the build-up work had already been completed. It was left to Murty to send the side out and he did so having made two changes from the draw with Ross County last weekend. Andy Halliday returned in midfield as Jon Toral dropped out, while Joe Garner also took a seat on the bench as Waghorn came into the Gers attack.

The Light Blue legions once again came out in their numbers but it was the sizeable travelling support that had a reason to cheer after just six minutes. This wasn’t the start that Murty would have hoped for.

Clint Hill failed to clear his lines and Halliday couldn’t either as Aidan Nesbitt fed the ball into the path of Michael Tidser. From the edge of the area, the midfielder beat Wes Foderingham with a low effort.

The Gers keeper should have done better, but that was of no concern to the Ton as they celebrated and dared to dream. Rangers had to respond.

It didn’t take long, either. Just six minutes later, Murty’s side were level as Miller once again stepped up to the plate.

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Barrie McKay had a big part to play as he burst towards goal and got a shot away. Keeper Derek Gaston couldn’t get the ball to safety and Miller was on hand to fire Rangers level.

It was a blow for Morton, but it wasn’t one that perturbed them. It has been a memorable campaign to date for Jim Duffy’s side and they once again went about their business efficiently at Ibrox.

Rangers almost doubled their tally through Emerson Hyndman as the midfielder tried his luck with a curling effort from the edge of the box but Morton weren’t exactly under siege as they game settled down again.

The Gers did have a couple of chances, both of which fell to Jason Holt, but they could breach the Ton defence again before the break.

The first saw Holt glance a header just wide from a Tavernier cross before the midfielder was just inches away from connecting with the ball after McKay burst down the left flank.

By the time Rangers finally got their second of the afternoon, Morton could easily have had theirs. Like on so many occasions this term, the Gers almost shot themselves in the foot.

A mistake from Philippe Senderos sent Nesbitt clear but the on-loan Celtic kid couldn’t capitalise. With only Foderingham to beat, he scooped his shot high over the bar.

It was to prove costly for Duffy’s side. Waghorn had seen a low effort go just wide of the far post after Nesbitt’s miss but he didn’t have to wait long for his goal.

A neat flick from McKay on the edge of the box sent Holt free. Hyndman helped the ball on at the near post and Waghorn was on hand to convert and put Rangers in the driving seat.

The Gers may have been ahead, but they were far from comfortable. The job wasn’t done yet.

As the clock ticked down, Morton’s confidence didn’t diminish as they continued to show why they are in the running for a Championship play-off berth this time. Clear chances were hard to come by for the visitors, but Jamie Lindsay almost found the top corner with an effort that had Foderingham flying to his left.

In the final seconds, Rangers should have had a third and could have lost a second. Waghorn could only direct his effort at Gaston after a McKay cross but it was at the other end that the drama almost unfolded.

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A mix-up between Foderingham and Lee Hodson, on for the final few minutes to replace the injured Lee Wallace, allowed Morton one final chance. It was spurned by Luke Donnelly as Morton’s dreams were dashed, his strike scooped over the bar as Foderingham and his defence scrambled to get back into position.

At the final whistle, Duffy’s players put their heads in their hands. For Rangers, it was pats on the back all round.

Having taken another step on the road to Hampden, Rangers will now look to kick-start their bid for second spot in the Premiership when they travel to Dundee on Sunday.

No matter who is in charge or who is selected, the requirement for victory is the same. One phase of the campaign is now over, and the second must be better.