It could have been worse for Rangers had substitute Ramon Pereira capitalised on a mistake by Jose-Karl Pierre-Fanfan in the closing moments but it mattered little in the grand scheme of things.
Victories for both Hearts and Celtic mean McLeish’s men now trail the league leaders by 11 points and Gordon Strachan’s men by eight and only the most optimistic of Rangers supporters would now stake money on Rangers retaining the league title won so memorably last May.
On a miserable night in West Lothian and with his striking options greatly diminished due to a rash of injuries, any sort of victory would have been acceptable for McLeish regardless of how it was achieved and, perhaps predictably given Rangers’ recent form, it wasn’t pretty.
With Peter Lovenkrands preferred to both Ross McCormack and Steven Thompson in the second striker role and Dado Prso continuing with his preference for patrolling the flanks rather than the penalty box it was hardly surprising that chances in a dismal first half were at a premium.
Rangers, just as they had done on Saturday, scored with their first real attack of the game although this time it took 14 minutes rather than 28 seconds to break the deadlock.
The goal stemmed from a Livingston throw-in deep in the Rangers half. Ian Murray stole possession and shovelled a pass wide to Burke on the right touchline.
Burke galloped into the penalty box, cut inside before finding Ferguson who trundled a low shot past Roddy McKenzie who seemed slow to react as the ball squeezed under his body.
Against the side anchored to the foot of the table, Rangers could have extended their lead five minutes later when Lovenkrands fastened on to a telling Ferguson pass but saw his shot ricochet off the body of McKenzie and away to safety.
That, however, was the last time the goalkeeper was called in to action before the break as Rangers failed to convert their possession into any real notable chances.
Marvin Andrews – back at his former club – thundered two headers narrowly wide following pinpoint crosses from first Burke and then Brahim Hemdani while Lovenkrands seemed to have a decent shout for a penalty after being wrestled to the ground by Greg Strong.
Livingston, as befitting a team without a league win to their name all season, offered little as an attacking force before the break but still did enough on occasion to serve intention of what was to follow later in the match.
Player-manager Paul Lambert screwed an effort well wide of the target from a promising position before Strong made space to thread a low shot through a crowd of bodies that Ronald Waterreus was happy to snaffle up.
Lambert chose to remove himself from the fray at half-time but the change initially failed to greatly alter the flow of proceedings and within eight minutes of the re-start Rangers had extended their lead.
Ian Murray and Olivier Bernard combined well down the left to create the opening and from the Frenchman’s enticing cross Burke slid in at the back post to score his second goal in consecutive games.
The strike should have been enough to finally kill off this impoverished Livingston side but instead they grabbed a lifeline just minutes later when Snodgrass surprised Waterreus with a speculative long-range drive that snuck into the corner of the net.
It would get worse for Rangers nine minutes later when a resurgent Livingston drew level.
The goal stemmed from a mistake by Pierre-Fanfan who found himself on the wrong side of James McPake as they contested a ball down the flank and left himself with no option but to haul the substitute to the ground.
Paul Tierney delivered the resultant free kick deep into the Rangers penalty box where Snodgrass was able to outspring his markers to flick the cross beyond Waterreus.
From a position of near total dominance Rangers somehow found themselves retreating onto the back foot as Livingston sensed the chance to collar their first league win of the season.
McLeish threw on Steven Thompson to try to boost his side’s options in attack but it was Livingston who threatened next, substitute Pereira almost capitalising on Andrews’ misplaced pass back to Waterreus.
Another Lovenkrands’ penalty claim – after a clash with the otherwise excellent Harald Pinxten – was waved aside before the Dane forced a great save out of McKenzie with a fierce drive from the edge of the box.
As the seconds ticked away, Pierre-Fanfan blazed an effort over the crossbar taking Rangers’ chances of securing all three points and possibly the title with it.
Only a great block from Waterreus denied Pereira a last-minute winner but by that time the damage had already been done.
RANGERS (4-4-2): 25 Waterreus; 2 Ricksen, 18 Pierre-Fanfan, 5 Andrews, 3 Bernard; 17 Burke, 7 Hemdani, 6 Ferguson, 24 Murray (Thompson 74); 9 Prso, 26 Lovenkrands
Subs not used: Klos, Alex Rae, Malcolm, Namouchi, McCormack, Hutton
Booked: Murray (6), Bernard (66)
LIVINGSTON (3-5-2):1 McKenzie; 4 Pinxten, 5 Strong, 3 Mackay; 7 Brittain, 8 Adams (McPake, 55), 35 Lambert (Barrett 46), 23 Walker, 15 Tierney; 12 Snodgrass (Pereira 81), 14 Scott
Subs not used: Roy, Adam, Miller, Boyd
Booked: Scott (22), Walker (74)