For weeks Alex McLeish had resisted the temptation to hand Burke a place in his starting line-up despite several eye-catching substitute cameos from the young winger.
The 20 year-old had been biding his time patiently on the sidelines since the start of the season but tonight he was like a wind-up toy that had been finally been let loose.
There was a buzz of expectation every time he received the ball and on most occasions he didn’t disappoint.
Burke had already sent over a succession of tantalising crosses and corners when he scored the most sublime goal after just 16 minutes.
Collecting a short pass just inside the St Johnstone half, he weighed up his options before speeding towards the penalty box where he executed an audacious chip over Kevin Cuthbert in the visitors’ goal.
To prove it was no fluke he almost repeated the feat just 10 minutes later, haring towards goal and leaving the trailing defenders bamboozled with a series of feints and step-overs.
Only the finishing let him down this time as he flashed a shot that bulleted narrowly past the far post.
By that stage and with St Johnstone virtual passengers to the one-way traffic, Rangers could and should have been further in front.
Egil Ostenstad, enjoying a rare start, had a thumping drive turned over by Cuthbert before a rampaging run by the Norwegian was illegally halted by Darren Dods.
Dods was booked and Vanoli’s free kick was well blocked by the keeper before Ostenstad rapped another low shot in that Cuthbert again parried well, although no Rangers player followed in to convert the rebound.
Last weekend’s goal hero Stephen Hughes then worked a cute 1-2 with Michael Mols but again the Saints stopper was equal to the effort and Rangers trooped in at half-time only one goal to the good.
For a team challenging for promotion near the top of the First Division, St Johnstone offered virtually nothing as an attacking force.
At 1-0 and with two men now picking up Burke’s every move, the Perth side were very much still alive in this cup tie.
Their chances of a comeback, however, died just short of the hour mark when Rangers grabbed their second of the game.
Vanoli made room to send over a spiralling ball and Ostenstad darted forward to power a header beyond the helpless Cuthbert.
St Johnstone finally called Allan McGregor into action after 73 minutes with the keeper having to get down well to block Dods’ downward header- although the linesman’s flag would have seen it ruled out in any case – before Rangers offered a late flurry of attacks.
Vanoli saw another free kick deflected wide for a corner before two headers from substitute Nuno Capucho both fell just the wrong side of the post.
With six minutes remaining, McLeish replaced Burke with Mo Ross and the 20 year-old departed the field to a deserved standing ovation. This had been his game.
Rangers then wrapped the game up with a last-minute goal from Mols who slid home Hughes’ pass from close range.
RANGERS (4-4-2): 22 McGregor; 2 Ricksen, 6 Malcolm, 5 Khizanishvili, 3 Vanoli; 7 Burke (Ross 84), 8 Hughes, 4 Emerson, 11 Lovenkrands; 10 Mols, 9 Ostenstad (Capucho 70)
Subs not used: Smith, Hutton, Gibson
Booked: None
ST JOHNSTONE (4-5-1): 1 Cuthbert; 2 J Robertson, 5 Dods, 6 Maxwell, 3 Forsyth; 7 Parker (Paatelainen 73), 8 M Robertson (Stevenson 35), 4 Bernard, 10 Donnelly, 11 McLaughlin (Malone 89); 9 Macdonald
Subs: Hay, Nelson
Booked: Dods (12), Forsyth (34)
Man of the Match: Chris Burke