A Nacho Novo penalty in the first half seemed to be the platform from which to build a convincing victory but instead it was the hosts who finished the stronger, equalising through substitute Daniel McBreen and even threatening a last-gasp winner.
By this time tomorrow, Rangers could find themselves trailing league leaders Hearts by eight points should George Burley’s men see off Livingston as they will be expected to do.
It left McLeish with much to contemplate ahead of Porto’s visit to Ibrox on Champions League duty on Tuesday evening.
Just as they had at Inverness the previous month, the Light Blues made heavy weather of breaking down a limited but well-organised Falkirk unit.
Sotirios Kyrgiakos returned to the line-up as part of a revamped 3-5-2 formation – the only ‘new’ signing to start the game – and while Rangers looked comfortable against a toothless Falkirk attack they offered little as an attacking force in a dreadful first half.
As a bitter autumn wind howled around the three-sided new Falkirk stadium, there never seemed a better time to champion the cause of summer football with little goalmouth action to warm the hearts of either set of supporters.
With 10 players battling for possession in the centre of the park and neither side exploring the wide areas with any regularity, the match descended into a largely scrappy and tense midfield encounter, with neither goalkeeper required to do much to earn their corn.
So little, in fact, did Ronald Waterreus have to do in a tedious first that he could have swung a hammock between his posts and enjoyed a quick afternoon siesta as Falkirk, missing playmaker Russell Latapy, toiled manfully without ever looking like scoring.
Their only real chance came courtesy of a misunderstanding between Krygiakos and Waterreus but, presented with his moment of glory, Alan Gow hesitated and the grateful goalkeeper snapped up the loose ball from the striker’s feet.
Not that Rangers were any more prolific at the other end. A Thomas Buffel sidefooted effort that drifted wide of goal after just 11 minutes offered early promise but that was it in terms of clear-cut chances until the Light Blues eventually went in front seven minutes before the break.
Predictably, given the stodgy nature of the match, it took a set-piece to break the deadlock.
A Fernando Ricksen hoist into the box was controlled by Buffel and as the Belgian accelerated on goal he was tugged back by Craig Ireland. Novo did the necessary from the penalty spot.
Rangers had the ball in the net again two minutes later when Buffel headed Barry Ferguson’s cross past the stranded Matt Glennon but the offside flag quickly curtailed the celebrations.
The second half was marginally better, no great achievement given what had taken place before it, and saw Francis Jeffers make his first Rangers appearance as a replacement for the tiring Buffel.
The former Everton striker looked sharp, linked up well with the midfield and the wide players and almost scored a debut goal shortly after coming on.
Dado Prso started the moved by sweeping a crossfield pass to Novo who in turn fed Ferguson. The skipper seemed to be steadying himself for a shot himself but Jeffers nipped in and thumped a fierce effort that Glennon did well to keep out.
In danger of being squeezed out the game, Falkirk boss John Hughes took the brave step of sending on two strikers in an attempt to rescue something from a game that was gradually slipping away from his side. His courage was rewarded within seven minutes when the hosts drew level.
The goal owed much to the quick thinking of Vitor Lima who, immediately after being fouled by Kyrgiakos, was on his feet to thread the free kick wide to Gow on the left.
With the Greek defender still out of position contesting the referee’s decision to award the foul, Rangers were exposed at the back and from Gow’s enticing centre substitute McBreen rose to nod his side level.
Temporarily stunned, Rangers were soon on the attack again and only an acrobatic block from Glennon stopped Ferguson from putting his side back in front, Kyrgiakos wasting the rebound opportunity.
Jeffers did have the ball in the net moments later but the offside flag again denied Rangers. The defence of the league title is getting more difficult by the game.
FALKIRK (4-5-1): 27 Glennon; 2 Lawrie, 25 Rodrigues, 6 Ireland, 15 Milne (McBreen 70); 5 Ross (McPherson 33), 22 S Thomson, 12 Scally, 18 Lima, 28 O’Donnell (Duffy 70); 8 Gow
Subs not used: Hill, A Thomson, McStay, Moutinho
Booked: McPherson (36), Scally (57)
RANGERS (3-5-2): 25 Waterreus; 18 Pierre-Fanfan, 16 Rodriguez, 14 Kyrgiakos; 2 Ricksen, 6 Ferguson, 4 Buffel (Jeffers 56), 31 Namouchi (Lovenkrands 81), 24 Murray; 9 Prso, 10 Novo
Subs not used: Klos, Andrews, Rae, Smith, McCormack
Booked: Ricksen (20), Ferguson (74)
Referee: Craig McKay
Key Man: Sotirios Kyrgiakos, A Solid Comeback