The Albion home ground is the only Irn-Bru Third Division venue at which the Glasgow giants have failed to emerge victorious this season after their first visit in October ended in a shock 1-0 defeat.
They have notched up nine successive away wins since that game but this performance showcased many of the team's frustrating frailties as Andy Little's 22nd goal of the season was allowed to be cancelled out by Ross Forsyth's 51st-minute equaliser.
The league leaders started the game a massive 37 points ahead of the second-bottom Binos and should have had enough to maintain their 22-point lead at the top, which has now been trimmed by two after Queen's Park's win over Clyde.
There was the small mercy for the Ibrox club in that their under-fire support remained largely muted following Saturday's controversial rendition of several sectarian anthems at Berwick.
The club look set to escape Scottish Football Association punishment for those outbursts but chief executive Charles Green will hope to avoid any embarrassing repeats as he strives to rebuild the club's international reputation.
A turgid second-half display and a chronic inability to defend crosses into the box cost Ally McCoist's men the victory this time, yet Rangers had looked hungry in the opening exchanges.
It was an intricate link-up between Dean Shiels and Little that sent the Northern Irishman through first time round but an offside flag was raised by linesman Graham McNeillie just as he put his shot wide of goalkeeper David Crawford's goal.
While Stirling caused Light Blue hearts to flutter after 14 minutes as striker Jordan White beat Emilson Cribari to Kieran McAnespie's free-kick only to head over, the two Rangers frontmen linked up again moments later and this time their timing was perfect.
Shiels collected a ball from midfield and was able to turn and face up to the Binos back four before slotting a finely-weighted pass in behind for Little to gallop onto.
With one touch to round the on-rushing Crawford, he took another to set himself before rolling the ball into the empty Stirling net.
The home side were nothing but plucky though and, not for the first time this year, Rangers' weaknesses at cross-ball situations were exposed as Allison - the man who consigned the Light Blues to their only league defeat of the season back in October - was found by another McAnespie set-piece.
He failed to repeat his heroics, however, as he headed wide of Neil Alexander's left-hand post.
Little was set free again by Kal Naismith's through-ball down the inside-right channel on 23 minutes but saw Crawford stand up to his shot, while the supplier of that chance - making his first league start for Rangers - was thankful to see Phil Johnstone blaze over for the hosts after gifting possession to Stirling.
But having had a couple of warnings in the first half, Rangers once again failed to learn their lesson as McAnespie swung another fantastic delivery into the box six minutes after the interval.
Full-back Anestis Argyriou had been penalised for a shove on Johnstone and with the free-kick, the former Hearts and St Johnstone midfielder picked out Forsyth to bullet home the equaliser.
Stunned by the goal, Rangers' fluid display of the first half had been replaced by an aimless succession of long balls up to Little.
The spark had gone but, with 20 minutes left, they almost found themselves back in front as Stirling right-back Jamie McCunnie was short with his chested back-pass to Crawford as Little lurked.
The Rangers goal-scorer got there before the keeper but put his shot into the side-netting.
Stirling could have heaped even more misery on their opponents as Mark Ferry shot just wide from McAnespie's headed flick on, while the midfielder proved himself useful at the other end as he headed clear from Rangers substitute Francisco Sandaza's volley after Ian Black had swung and missed at a bouncing ball in the six-yard box.
There was another scare for the Rangers support as McAnespie had a late free-kick pushed away by Alexander, while Little could have made himself a real hero had he done better than send a volley straight at Crawford at the death.