Rangers eventually wore down a resolute Raith Rovers side to run out comfortable 3-0 winners in a mostly low-key Scottish Cup quarter-final tie at Ibrox.
The Championship side defended from the first whistle and nullified the Gers threat until the 42nd minute when defender Connor Goldson headed in from a Borna Barisic corner.
Rovers defender Ryan Nolan scored an own goal in the 58th minute to effectively end any chance of a shock before substitute Scott Arfield added a third for Michael Beale’s side with three minutes remaining.
The cup holders join Celtic, who just last month beat the Light Blues in the Viaplay Cup final, Championship side Inverness and the winners of Monday night’s Falkirk versus Ayr clash in the last-four draw.
How Rangers reached the last four…
Beale promised to play his strongest team and made only one change, midfielder John Lundstram in for Ryan Jack, while left-back Ridvan Yilmaz was back on the bench following his long-term hamstring injury.
However, the visitors came close to taking an early and unlikely lead.
There was just over a minute gone when Goldson’s slack pass was intercepted in the centre circle by Rovers striker Esmael Goncalves and his lobbed shot was not too far off-target, with ‘keeper Allan McGregor out of his goal.
The Kirkcaldy men retreated into their own penalty area and asked Rangers to break them down.
In the 10th minute, Rovers ‘keeper Jamie MacDonald made a fine save at his near post from James Tavernier’s drive after the Gers captain had played a one-two with Lundstram.
However, Rangers were finding it tough to get through the packed defence.
As their side toiled, Gers fans became increasingly frustrated at the amount of times Rovers players required attention for injuries.
However, the breakthrough came just before the break when Goldson leapt at the back post to bullet in a header from Barisic’s delivery.
Without the usual noise from the Rangers fans’ group the Union Bears – Rangers revealed they had boycotted the game in protest as the club “would not permit the offensive anti-police banner display” – the atmosphere remained flat going into the second half.
Rangers kept going and added a second just before the hour-mark when the luckless Nolan’s attempted clearance from a Tavernier cross ended up behind MacDonald.
The visitors began to tire as the holders pinned them back although they came close when Aidan Connolly’s cross from the left was missed by Goncalves at the back post.
Rangers made a triple substitution with Yilmaz back for the first time since October, coming on with John Souttar and Arfield for Goldson, Barisic and Fashion Sakala before McGregor foiled substitute Ethan Ross, just on for Goncalves.
MacDonald thwarted Arfield at his near post, diving to block a drive and it became a case of Rovers trying to prevent the scoreline from being stretched.
In the 79th minute, Antonio Colak and Ryan Kent made way for Alfredo Morelos and Ianis Hagi but in the 87th minute, it was fellow substitute Arfield who took a pass from Todd Cantwell to knock the ball past MacDonald.
What the managers said…
Rangers boss Michael Beale was pleased to see Rangers overcome a different type of challenge to get past Raith Rovers.
He said: “We’ve played three games this week and faced three different types of challenges, today Raith tried to make the game really difficult by staying in.
“We had 18 corners, 24 shots. When the first goal goes in from a corner the game you hope it opens up a bit but it didn’t, they stayed disciplined and stuck to their task so it made for a slow game.
“Although it was our third game in a week I’d like us to be a little bit sharper in and around the box.
“I thought Borna Barisic put in some fantastic crosses today and we need people to go in and challenge for those. But it was a slow game, there were a lot of niggly injuries, and I’m just glad we’re through to the semi-final.
“They were really deep and I can’t choose how the other team approach the game, we can only face the problems that are put in front of us.
“In midweek Hibs came and tried to face us head-on and left spaces and we were really ruthless. Raith tried a different tactic of being really compact in the game. We still got into really good areas and I’m expecting us to do slightly better. But the way they played the game we had to see it out professionally and we did that in the end.
“After the high of Wednesday, we had to go through that one today and the most important things were a clean sheet, three goals and we move on.”
Raith Rovers boss Ian Murray was proud of the way his depleted side performed.
The former Rangers player said: “We are disappointed to be out of the Scottish Cup. We wanted to go further obviously.
“But my emotion right now is pride in the football players, I thought they were excellent.
“I thought the discipline and the shape and structure they carried out was great.
“Also pride in the supporters we brought today and the appreciation they showed us towards the end.
“But to a man, I thought our players gave everything within the game.”
The semi-final draw for the Scottish Cup will take place on Monday night.
Rangers return to Scottish Premiership action on 18 March away to Motherwell, live on Sky Sports. Kick-off 12.30pm.