The country’s lowest placed club at the start of proceedings were without their manager, who was getting married, but captain Brian Allison’s eighth minute goal was enough to earn them a famous victory.
Rangers dominated the second half of the match at Forthbank but didn’t cause enough problems to turn around the early deficit.
A tetchy first half saw three of the home side booked and Steven Weir luck to stay on the pitch when his two footed lunge at Alexander resulted in only a yellow card.
By that stage the visitors already found themselves behind to Brian Allison’s eighth minute opener.
A corner swung in to the box wasn’t dealt with and when McAnespie’s poor header dropped to Allison he did enough to poke it home beyond Alexander.
McAnespie was the first of the home side’s players to see yellow within minutes when he felled Anestis Argyriou on the right flank.
Fraser Aird, who looked the most threatening for Rangers in the opening 45 minutes, joined him in the book ten minutes later when he caught David McClune on the opposite wing.
The young midfielder almost produced the moment that drew the visitors level on 24 minutes when his delivery was flicked on by the head of McCulloch.
Unfortunately the skipper’s glancing effort cannoned back off the post and Argyriou was unable to scramble it in at the far post.
Almost immediately at the other end the home side had a chance to extend their lead when Jordan White’s effort was deflected by Emilson Cribari
Weir clearly felt the ball was there to be won and clattered in to Alexander, leading with both feet, and was lucky to escape with only a caution.
Aird and White then exchanged shots that were dragged across the face of the goal on 32 and 36 minutes respectively.
Black’s mistake then almost presented Weir with another chance, the midfielder holding his hands up to the error.
After Argyriou then passed up a chance at the other end ,McCulloch did find the target from a free kick, but Sam Filler was equal to the effort.
McClune completed the administration for referee Bobby Madden in the opening period when his late trip on Shiels on the half way line saw him become the fourth player cautioned in the first half.
Ally McCoist’s words at the interval had an early effect with Shiels and Aird both going close in an opening ten minutes that suggested the momentum would swing in Rangers’ favour.
The closest they came however was a clearance off the line as Marc McCulloch denied Sebastien Faure, clearing the Frenchman’s header from Shiels’ delivery.
That came in the 54th minute and it speaks volumes that it was the closest Rangers came in the second half.
Despite maintaining the majority of possession throughout that second 45 minutes they couldn’t exert the pressure McCoist would have wanted to see.
The introduction of Barrie McKay added a much needed spark, but his effort over the bar was the closest he came to influencing the result.
It almost fell to fellow sub Kevin Kyle to fulfil that job as he was played in on the edge of the box only to fire his effort straight at sub keeper Mark Peat with four minutes remaining.
Shiels almost levelled in the dying moments but his effort was wide as he ran on to a cutback from Macleod.
RANGERS: Alexander; Faure, Perry, Cribari, Wallace; Argyriou (McKay 67), Black (Naismith 85), Macleod, Aird (Kyle 71); Shiels, McCulloch.
SUBS: Gallacher, Crawford.
BOOKED: Aird, McCulloch.
STIRLING ALBION: Filler (Peat 46), McClune, McAnespie, McCulloch, Thom, Allison, G.Weir, McSorley (Day 59), White, S.Weir (Flood 88), Ferry.
SUBS: McGeachie, Brass.
GOALS: Allison (8)
BOOKED: McAnespie, S.Weir, McClune, Thom
REFEREE: Bobby Madden