The second-half, however, was a different story and when Ross Forsyth bagged a headed equaliser on 51 minutes Greig McDonald’s side gained confidence and more than matched the visitors despite being second bottom of the division.
McCoist made two changes to his starting eleven with Emilson Cribari returning to the line-up with Ross Perry expected to be out for several weeks with a hamstring injury.
Kal Naismith also made his first league start, taking the place of Barrie McKay who was hooked at half-time during Saturday’s victory over Berwick.
Rangers endured a bruising battle when they last travelled to this venue with the Binos producing several poor tackles on their way to a shock victory.
At the start of tonight’s match a similar no-nonsense challenge by Josh Flood on David Templeton after just 1 min 40 seconds left the winger writhing in pain. Ref Graham McNeillie, however, decided against booking the number 10 to the frustration of the travelling Bears.
This certainly fired up the visitors and in the first-half McCoist would have been happy with how his players applied themselves on a frosty and slippery surface.
On five minutes Kal Naismith was brought down 20 yards from goal and vice-captain Lee Wallace stepped up but blazed his free-kick over the bar.
On loan forward Jordan White then had a chance to open the scoring for the home side but his glancing header from eight yards missed the target.
This was only a minor scare and when play resumed Rangers continued in the search for an opening goal which Little scored, taking his tally to 22 for the season.
Dean Shiels played the ball through to his in-form strike partner who, having beat Stirling’s offside trap, rounded keeper David Crawford before calmly rolling the ball home from a tight angle.
The goal took Little level with Lee McCulloch at the top of Gers’ scoring charts and he’s clearly relishing his current role in attack.
On 23 minutes, however, he had a great opportunity to double his side’s advantage when he latched on to Naismith’s pass down the right channel but his low drive was saved by Crawford who used his legs to make a crucial stop.
60 seconds later and the official had to go to his top pocket to pull out a yellow card when Flood again halted Templeton’s progress unfairly.
Cribari then received a similar punishment for a late challenge from behind on Albion winger Phil Johnston.
Rangers were unable to extend their lead before half-time but before the ref’s whistle they produced an excellent move which cut open Stirling’s defence.
Wallace played the ball to Shiels on the edge of the 18-yard box before continuing his run.
The forward’s intelligent back-heel then went through the legs of his marker but Wallace’s left-foot shot went high and wide.
In to the second half and again Rangers started well with Little carving out a couple of opportunities with determined play on the right wing.
But on 51 minutes Stirling showed their fighting spirit and made the most of poor marking to net a well-worked equaliser.
Kieran McAnespie’s excellent free-kick found Forsyth who produced a bullet header beyond Alexander who could do nothing as it flew past him into the net.
With the hour mark approaching the hard work put in the first half was now forgotten about and it was fast become a slog with the Rangers fans becoming increasingly frustrated with their team’s poor passing, particularly in the final third.
Little, however, was a constant threat and on 68 minutes the Ulsterman intercepted a chested back pass from David McClune but after again skipping past the keeper the angle this time proved too tight for the tenacious forward.
Next up it was Naismith’s turn to create an opening but after stepping over the ball his left foot shot was straight at Crawford.
With 18 minutes remaining McCoist made a double switch with McKay and Sandaza replacing Templeton and Shiels respectively.
Stirling, however, continued to push forward themselves and a powerful effort from Mark Ferry from 20 yards went inches wide of Alexander’s far post with the keeper at full stretch.
At the other end Black failed to connect with the ball as it dropped to him in the box with only Crawford to beat. It then fell to Sandaza but his goalbound effort was headed off the line by Ferry.
Stirling’s McAnespie attempted two long range free kicks as the clock ticked down – the first was saved by Alexander and the second went over the bar – but neither team could find the net at the death with Little guilty of missing a snip after he was teed up by Naismith in injury time.
Rangers are now 20 points clear at the top of the Third Division after second placed Queen’s Park beat Clyde 3-0 at Broadwood tonight.
STIRLING ALBION: Crawford, McCunnie, Forsyth, McClune, Allison, Bishop, McAnespie, Ferry, White (Cunningham 90), Flood (Ashe 46), Johnston
SUBS: Filler, Davidson, Thom
BOOKED: Flood, Allison, Forsyth
RANGERS: Alexander, Argyriou, Cribari, Hegarty, Wallace, Naismith, Black, Hutton, Templeton (McKay 72), Shiels (Sandaza 72), Little
SUBS: Gallacher, Crawford, Faure
BOOKED: Cribari, Naismith, Hutton, Hegarty
REF: Graham McNeillie
ATTN: 3, 707