Rangers had approached the weekend knowing they could be celebrating the Irn-Bru Third Division title, but they were greeted with boos from a dwindling Ibrox crowd at the final whistle after failing to put Albion under any sustained pressure.
The prospect of the title win disappeared hours before the noon kick-off when second-placed Queen's Park saw their clash at Annan postponed because of snow and it was just as well for Rangers as they had needed a victory. Apart from a couple of early chances, Rangers did not look like getting the breakthrough and Stirling came closest when Jordan White had a header cleared off the line.
Rangers' two best chances came in the first quarter. Lee Wallace had the first one inside six minutes when he played a one-two with Kane Hemmings that put him clean through, but Stirling goalkeeper Sam Filler made himself big enough to block the left-back's attempt to dink the ball home.
Hemmings then missed a good chance when he headed over Barrie McKay's right-wing cross, and he also dragged a shot wide just before the half-hour mark following a rare sharp passing move from the hosts. Wallace had set that chance up with a first-time pass and the left-back looked the most likely Rangers player to open up Stirling.
But the visitors were not sitting back and were passing the ball around well at times. And they finished the half on top as they created two excellent chances. Striker White had a free header following Scott Davidson's corner and glanced the ball towards the far corner. Goalkeeper Neil Alexander was beaten but Fraser Aird headed off the line.
White then returned the favour to Davidson in the last move of the half, his cross finding the midfielder in yards of space just inside the box. However, Alexander raced off his line to put him off and the left midfielder fired just over. Fraser Aird forced a save from Filler just after the break with a run and shot but there was no second-half improvement from Rangers.
Davidson had another chance just before the hour mark when Phil Johnston's cross reached him at the back post, but the wide man's acrobatic volley took a deflection and seemed to be going wide before Alexander made sure.
The home side could still not impose themselves on the game with Stirling continuing to look threatening when they went forward while holding out comfortably.
Rangers are now four points from securing the title and could do so next weekend, but will need Queen's Park to slip up at home to Elgin after they play Montrose.