While there were eye-catching performances throughout the side, special mention must go to 19 year-old Alan Hutton who put in a sparkling shift in the right-back role.
McLeish had been hinting for weeks that Hutton was on the brink of a top-team start and the young Scot was one of three changes from the team that was held to a 1-1 draw at Tynecastle the previous week.
Zurab Khizanishvili returned to the side in the heart of the midfield in place of the suspended Fernando Ricksen with Steven Thompson deemed fit enough to lead the line up front.
With every player effectively now performing auditions for the right to be part of the Rangers show next season, there was no shortage of endeavour on show and the inclusion of four Scots in the starting line-up perhaps indicated the way McLeish intends on taking his squad forward.
Against an ineffective Dundee team, the Light Blues dominated from start to finish and were well worthy of their victory.
Hutton was a particularly dangerous threat down the right wing and he was largely instrumental as Rangers almost went in front after just 16 minutes, with Peter Lovenkrands latching onto his deep cross and toe poking in an effort that trickled just wide.
The Dane was unfortunate on that occasion but should have scored five minutes later when he planted a header straight at Julian Speroni from Ronald de Boer’s pinpoint cross.
It was the final contribution from the senior of the de Boer twins who had earlier suffered a bloody nose in an accidental collision with Tom Hutchinson and he was replaced by Michael Mols with just 25 minutes played.
Dundee offered very little, with even their prolific striker Nacho Novo stifled by the close attentions of the Rangers defence.
Only one time – after 10 minutes – did the Spaniard break free of his markers but presented with a golden chance to beat Stefan Klos he dragged a tame shot wide.
The rest of the match belonged to Rangers and Speroni had to plunge low to his left to keep out a thumping Thompson header from another Hutton centre before Gavin Rae looked certain to net after 40 minutes only to see Dave Mackay make a desperate goalline clearance to hack his former team-mate’s volley away from danger.
A minute later and Rangers finally broke through although the goal was shrouded in controversy.
Stephen Hughes’ cross was headed back across goal by Craig Moore, Frank de Boer nodded the ball over the goalkeeper and Lovenkrands lashed a shot into the empty net from a matter of yards.
The linesman’s flag seemed to have cut short the celebrations but after a consultation with referee Alan Freeland the goal was allowed to stand.
Buoyed by their lead, Rangers emerged from the tunnel in the second half and blew Dundee away, scoring three more goals and playing some of their best football of the season in the process.
Just two minutes after the re-start they doubled their lead. Rae was chopped down 25 yards from goal allowing Frank de Boer the chance to swagger forward from defence and nonchalantly swerve the free kick low to Speroni’s left and into the net.
With Klos probably now wishing he had brought a hammock and a good book out with him, Bob Malcolm – a half-time replacement for Craig Moore – headed wide from Michael Ball’s corner before the defender himself had a long-range effort collected by Speroni at the second attempt.
Dundee then survived a penalty claim when the ball struck Jonay Hernandez on the arm before Rangers sealed the win with two goals in the last minutes.
Rae – on his home debut – rattled in a fine right-footed strike from the edge of the box after 80 minutes before Thompson rounded off the scoring two minutes later after good work from Hutton and Mols.
Mols could have added a fifth a minute later when he battered a Thompson centre off the crossbar as Dundee crumbled in the face of ceaseless Rangers attacking.
This season may be over for Rangers but the future is looking bright.
RANGERS (4-4-2): 1 Klos; 28 Hutton, 5 F de Boer, 3 Moore (Malcolm 46), 18 Ball; 11 Rae, 27 Hughes, 15 Khizanishvili, 26 Lovenkrands (Burke 68); 14 R de Boer (Mols 25), 19 Thompson
Subs not used: McGregor, Malcolm, Vanoli
DUNDEE (5-3-2): 1 Speroni; 3 Mackay, 19 Mair, 4 Hutchinson, 18 Sancho, 16 Hernandez; 30 Fotheringham, 23 Barrett (Brady 53), 21 Robb (Lovell 46); 5 Kneissel (Milne 65), 17 Novo
Subs not used: Soutar, Cameron
Booked: Barrett (46)
Man of the Match: Alan Hutton