Against an impoverished Dundee side languishing around the foot of the table and unable to name a full quota of substitutes, McLeish watched his side race into a two-goal lead within four minutes that they rarely looked like relinquishing in the 86 minutes that followed.
A thunderous strike from Bob Malcolm early in the second half ended the match as a contest and sent Rangers back on top of the SPL – for 24 hours at least.
This was an afternoon of change for Rangers in many respects. There was the rare opportunity for the supporters to sample a traditional Saturday 3pm kick-off for the first time since August 21 while there was also a refreshingly youthful look to the substitutes bench with Lee Robinson, Brian McLean and Graeme Watson all promoted from the youth ranks.
On the debit side, there was the unusual sight of a Rangers side lining up without Jean-Alain Boumson in their numbers, the Frenchman having failed to shake off a thigh strain picked up in the previous week’s draw with Inverness Caley.
In his absence, Malcolm dropped back to partner Marvin Andrews in the heart of the defence allowing Dragan Mladenovic a return to the first team for the first time since September 19.
If Dundee had hoped the various alternations would disrupt Rangers’ rhythm then they would be swiftly disappointed as the Light Blues raced into an early two-goal lead.
The warning signs had been posted within just 40 seconds when Dado Prso volleyed a searching Zurab Khizanishvili pass over the crossbar but less than a minute later Rangers were in front from the penalty spot.
Gregory Vignal – returning to the side for the first time since November 25 – embarked on one of his typically jinking runs before swerving in a cross that rebounded to Nacho Novo on the edge of the box.
The former Dundee striker snaked inside Jonay Hernandez who instinctively threw out an arm to prevent the Spaniard from haring in on goal.
Referee Mike McCurry hesitated momentarily before awarding the spot kick that Novo duly converted for his 15th goal of the season – and his third against the club he left just last summer. So much for sentiment.
After the disappointment of that draw against Caley six days previously, Rangers looked determined to make instant amends and with less than four minutes played they were two goals in front.
Novo this time was the creator with a deep cross that was expertly controlled by Prso. The Croatian then sidestepped a clumsy challenge from Stephen McNally to afford him the space to thump the ball past the exposed Derek Soutar.
Complacency seemed to be Rangers’ most dangerous opponent at this juncture and, perhaps thinking the game already won, they allowed Dundee an opening to try to claw their way back into a match that should have already been beyond them.
Three times within 11 minutes Steve Lovell was awarded the space to launch strikes on Stefan Klos’s goal although, fortunately for Rangers, none of the trio of efforts were accurate enough to find the back of the net.
Dundee’s most telling opportunity, however, fell to Brent Sancho after 18 minutes when Steven Robb’s pinpoint cross presented him with a free header just yards from goal.
With the target at his mercy though the Trinidadian contrived to nod the ball straight into the grateful arms of Klos.
Perhaps relieved by the let-off, Rangers seemed to find their second wind and a third goal looked likely when a crisp Novo pass sent Prso thundering into the penalty box.
For all his talents, lightning pace is not a weapon in the Croatian’s armoury and he dithered long enough for McNally to slide in to clear the danger.
Moments later and Shota Arveladze’s header crept narrowly past Soutar’s far post as Rangers looked for a third goal before the goalkeeper did well to block a powerful Prso drive with his legs.
It was the visitors, however, who enjoyed the final opportunity of the first-half. Fabian Caballero robbed Vignal on the edge of the box and fed Neil Barrett whose shot appeared to be expertly tipped around the post by Klos only for McCurry to award Gers a goal kick.
Just as they had managed in the first half, Rangers scored early after the break to ultimately end any thoughts of a Dundee comeback.
The goal came from an unlikely source. Fernando Ricksen’s corner was headed out as far as Malcolm and although his first effort was blocked he tried again with a fierce left-foot half-volley that flew past Soutar.
Perhaps the only thing more surprising than a goal from Malcolm – his first ever at Ibrox – was the sound of the theme tune from cult cartoon Spongebob Squarepants echoing around the stadium as the players trotted back to the halfway line.
And that was that. Rangers did have the ball in the net once more – Prso was adjudged to have been offside – and both sides saw goalbound efforts cleared off the line but the match was effectively over as a contest.
Three goals, three points and three years provided the ideal anniversary present for McLeish.
RANGERS (4-4-2): 1 Klos; 15 Khizanishvili, 12 Malcolm, 5 Andrews, 24 Vignal (S Smith 79); 31 Namouchi, 2 Ricksen, 14 Mladenovic, 7 Arveladze (A Rae 63); 10 Novo, 9 Prso
Subs not used: Robinson, Ball, McLean, Watson, Hutton
Booked: None
DUNDEE (4-4-2): 1 Soutar; 20 McNally, 3 Sancho, 17 McDonald, 16 Hernandez; 12 Brady, 2 Smith, 14 Barrett, 18 Robb; 9 Lovell (Credeira 76), 26 Caballero (Larsen 67)
Subs not used: Murray, Sutton, Jablonksi, Mann
Booked: None
Man of the Match: Bob Malcolm