The Albion home ground is the only Scottish 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.
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 Andy Little that sent the latter 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, and with one touch to round the on-rushing Crawford, he took another to set himself before rolling the ball into the empty Stirling net.
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 Phil Johnstone and with the free-kick, the former Hearts and St Johnstone midfielder picked out Ross 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Stunned by the goal, Rangers' fluid display of the first half had been replaced by an aimless succession of long balls up to Little.
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.