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.
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 was 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.
