Gers booked that place at the national stadium following a relatively straight-forward three-goal victory over a Pars side that offered little of an attacking threat throughout a sterile 90 minutes.
Jimmy Calderwood’s side had made for stern opposition when the teams had met in the original quarter-final tie a fortnight ago but they were a pale imitation of that in this replay.
History, admittedly, had not been on their side.
Dunfermline hadn’t won at Ibrox for almost 31 years and with just three minutes gone you suspected they weren’t going to break the hoodoo on this occasion.
It had taken a full 70 minutes for Partick Thistle’s resistance to be broken in the previous match at Ibrox. Dunfermline couldn’t hold on for even a fraction of that.
Goalkeeper Derek Stillie had been the main difference between the sides in the original side with a batch of breath-taking saves but he was the villain of this particular cameo with a weak throw-out that fell kindly for Peter Lovenkrands, via the boot of Andrius Skerla.
The Whippet needed no second invitation to take advantage, racing in on goal before placing a shot behind the red-faced goalkeeper.
Aside from an early chance when Steven Hampshire slid the ball wide of goal, this was a tame performance from the Pars in comparison to the endeavour they had showed in the first tie where they had attacked with relish.
In front of the lowest crowd of the season, Rangers were in cruise control and should have doubled their lead after only six minutes.
Barry Ferguson had been greatly missed in the struggle to see off Thistle but he was in thick of the action on his return and should have found the target from the edge of the box after de Boer had contested a loose ball with Stillie.
The Rangers skipper made amends from his miss on 19 minutes when he doubled Rangers’ lead.
Arthur Numan – making his first appearance since February 22 – fired over a perfect cross that Ferguson powered past the goalkeeper by way of a spectacular diving header.
There was little else to warm up the home crowd on a chilly evening although Dunfermline could have given cause for concern if Barry Nicholson had converted a pass from Brewster just before the break.
It looked as if Stefan Klos had pulled off a tremendous fingertip save to turn the ball around the post but a goal kick was the referee’s assistant’s decision.
The German goalkeeper has been an unsung hero for the Light Blues for the duration of the season but, not surprisingly, was content not to take the plaudits this time around as well.
It was a similar story in the second half as well with Michael Mols and Lovenkrands going close before some more de Boer magic ended the game as a contest after 53 miutes.
Bert Konterman shoved the ball through to his Dutch counterpart who made space to slide a pass to the on-rushing Mikel Arteta.
The Spaniard dinked the ball over Stillie and the ball dribbled over the line despite Skerla’s best attempt to clear the danger.
It was Rangers’ 100th goal of the season and Arteta’s first at Ibrox and was much deserved after an impressive performance from him.
Play petered out after that – sub Shota Arveladze rattled the crossbar in the closing moments – and not even the introduction of Noel Hunt could spark a Dunfermline revival as Rangers ran down the clock to book another date at Hampden.
RANGERS (4-3-3): 1 Klos; 2 Ricksen, 4 Amoruso, 12 Malcolm, 5 Numan (McCann 65); 6 Ferguson (Arveladze 72), 23 Arteta, 15 Konterman; 10 Mols, 14 de Boer (Caniggia 66), 26 Lovenkrands
Subs not used: McGregor, Hughes
Booked: None
DUNFERMLINE ATHLETIC (4-4-2): 20 Stillie; 21 Bullen, 2 McPherson (Kilgannon 46), 5 Skerla, 16 McGroarty; 7 Nicholson, 8 Mason, 11 Brannan (Grondin 72), 12 Hampshire; 9 Crawford, 10 Brewster (Hunt 61)
Subs not used: McGarty, Ruitenbeek
Booked: Grondin (81)
Man of the Match: Ronald de Boer