Goals from Andrius Velicka, Kris Boyd and Kenny Miller eased Walter Smith’s men through to that point on May 30, where they’ll meet Falkirk or Dunfermline.
It was nervy for a while as Gers gave Saints space to play after Velicka’s early opener but they sealed their passage midway through the second period and were deserved victors.
The high point was Boyd’s 100th goal for the club – but there was a low too as Pedro Mendes was carried off in agony shortly before the break.
It remains to be seen how badly hurt he is at this stage but whether he plays any further part this season has to be in doubt.
Manager Smith went with the same team that beat Motherwell 3-1 a fortnight ago at Ibrox.
That meant there was just one change to the side that won at Hibs last week, with Christian Dailly replacing the suspended Sasa Papac.
Goalkeeper Allan McGregor also returned to the squad and took a seat on the bench at Graeme Smith’s expense.
Indeed, he found himself in the very same dugout as the one where his actions whilst representing Scotland at the start of the month led to a two-week club suspension.
Having lost just once in their 17 previous Scottish Cup clashes with St Mirren, the odds were certainly stacked in Rangers’ favour.
So too was the fact they went into the match unbeaten in their last 20 semi-finals in the competition.
The Light Blues have made a habit of starting games well lately and ahead of this one, they had scored in the opening eight minutes in each of their last four matches.
Sure enough, they kept that impressive run going with yet another electric start as they took the lead after just 74 seconds.
Steven Davis played a perfectly-weighted pass through to Boyd in the box and he shot but Will Haining was there to block.
The rebound only went as far as Velicka and he was able to drill high into the net from six yards.
That brought his tally to three goals in as many games and the comeback he has made after finding himself well out of the picture at Ibrox has been quite remarkable.
Saints tried to come back from their early setback and enjoyed a decent amount of possession.
But it was Gers who almost netted again through Mendes, with Mark Howard tipping his shot from 20 yards wide after Velicka’s lay-off.
The Buddies’ response was positive, with Neil Alexander having to react well to tip over a swerving Steven Thomson piledriver from 30 yards.
Davis also needed to be in the right place at the right time to block Haining inches from the line when the big defender tried to force the ball home.
Mo Edu was perhaps fortunate to stay on the park when he reacted to Stephen McGinn’s approach after the American left a foot in as the two went for a loose ball.
But the Paisley player was just as lucky given he was the aggressor and it took sensible refereeing from Calum Murray to diffuse the situation.
Boyd came close to reaching his personal milestone when Dailly dug out a cross on the right and the hitman headed just over.
But it was a quiet first half otherwise and chances were few and far between as the action threatened to become a little too pedestrian at times.
Temperatures soon rose a few minutes before the interval when Haining and Mendes challenged each other and the Portuguese midfielder came off far worse.
Having apparently hurt his right knee, the former Portsmouth star was carried off on a stretcher in some discomfort after treatment on the pitch.
Nacho Novo came on in Mendes’ place as he was taken down the tunnel and the sight of him in such pain was a clear concern.
Davis was pushed into central midfield and one of his first acts was to release Velicka, whose finish under pressure from Mo Camara was poor.
The second half began with St Mirren fans claiming for a penalty when Steven Whittaker slid in on Andy Dorman as he made his way into the box.
As it was, the full-back made a fantastic tackle and won possession to stop the highly-rated midfielder in his tracks.
Velicka and Novo both had opportunities to extend Rangers’ advantage, although neither of them were particularly troublesome.
But while Smith’s men were carving out more up front, it seemed they would need a second to make sure of their progression to the final.
They weren’t playing well and that was a worry as Gus MacPherson’s team started to look more dangerous around the hour mark.
The Light Blues tried to up the tempo and they threw on fit-again Miller for the labouring Velicka.
But it was Davis who engineered the goal that doubled the lead when he burst through the heart of midfield to set up Boyd.
The ex-Fulham midfielder’s lung-bursting run allowed him to set up the striker and he completed his century with a cool finish.
Just three minutes later it was 3-0 as Novo, Davis and Miller all combined for the latter to fire in his 12th goal of the season at the end of a nice move.
With that, Rangers knew they were through at last and Boyd went off to a standing ovation as young Andrew Little was thrown on for his first-team debut.
Now he and his team-mates can look forward to being there at the season’s climax next month – and they’ll hope they’ll be out to add the trophy to the SPL title by then.