They battled hard against Livingston without really exerting any sustained pressure and it could have been even worse for the Light Blues had Stefan Klos not saved a first-half penalty.
The mid-week endeavours against Manchester United appeared to have taken their toll on McLeish’s squad, with Shota Arveladze, Michael Mols and Peter Lovenkrands all ruled out of action while Henning Berg dropped down to the bench.
The enforced changes meant recalls for Nuno Capucho, Emerson and Christian Nerlinger while Egil Ostenstad was handed his first start since moving to Ibrox in the summer.
With Capucho preferring to patrol a channel wide right on the touchline, the Norwegian striker was often left to fend for himself in a lonely role up front against Livingston’s powerful back three.
He had a useful game as the link man and was involved in creating most of Rangers’ best opportunities in what was another stop-start performance from McLeish’s men.
As has been the norm in recent weeks, they sprung out of the blocks – Mikel Arteta tested Roddy McKenzie with a blazing drive after just 80 seconds – but once again they were unable to sustain any real pressure and allowed their hosts gradually back into the game.
With Livingston threatening more through the ever-dangerous David Fernandez, Rangers had Klos to thank for keeping the scores level after 20 minutes when he dived low to his left to expertly block Lee Makel’s penalty after Fernando Ricksen had tumbled into Jamie McAllister.
Buoyed by that let-off, Rangers poured forward and Arteta came close with dangerous free kicks twice in quick succession.
Livingston were no spectators either and Klos denied Makel with another fine stop before David McNamee had a goal chopped off for an earlier handball decision.
McLeish chose to go Scottish in the second half as he introduced Stephen Hughes and Chris Burke as substitutes to try to carve out a scoring opportunity.
Arteta had a penalty claim waved away before the Spaniard dragged a shot well wide from Capucho’s lay-off.
Rangers were again enjoying the majority of the possession without really testing McKenzie in the Livi goal, although the keeper had to look sharp to twice deny Ostenstad.
With just two minutes remaining, the Light Blues passed up their best chance of the game.
Craig Moore powered forward from defence to play a perfect through ball to Capucho who chose to come in on his right foot before shooting wide from just 12 yards out.
The Livingston support burst into song knowing their team had done enough to earn a point.
LIVINGSTON (3-5-2): 18 McKenzie; 6 Dorado, 5 Andrews, 4 Rubio; 2 McNamee (McGovern 80), 17 Lovell (O’Brien 65), 21 Kerr, 14 Makel, 3 McAllister; 7 Fernandez, 16 Lilley
Subs not used: Findlay, Walker, Arthur
Booked: McNamee (23), Makel (26), Dorado (37)
RANGERS (4-4-2): 1 Klos; 2 Ricksen, 15 Khizanishvili, 3 Moore, 18 Ball; 23 Arteta, 4 Emerson (Hughes 46), 8 Nerlinger (Burke 64), 16 Vanoli; 9 Ostenstad, 20 Capucho
Subs not used: McGregor, Ross, Berg
Booked: Moore (23)
Man of the Match: Mikel Arteta