The Glasgow side celebrated 140 years of existence with a win over their opponents, who had Daly McSorley sent off before Andy Little confirmed the points in the final moments
David Templeton and Andy Little were on hand to nab the goals for the hosts, but they had to leave it until late on to confirm the points, with Little grabbing his goal in injury time after Daly McSorley saw red for the visitors.
The game was fiery from the off, with Mark McCulloch picking up a booking in the first minute for a nasty tackle on Templeton, but it was all Rangers from then on as the home side squandered chance after chance in the opening 45 minutes,
Kevin Kyle and Templeton combined well after nine minutes to set up Lewis Macleod, but his fierce drive was just wide of the post. Nine minutes later Kyle met a cross at the back post to set up Kyle Hutton, but his shot bounced over.
Five minutes before the interval Rangers went closest, with Kyle beating the Binos keeper, but he saw his effort crash off the post as McCoist's men searched for the opener.
At the interval fans were treated to a parade of club legends to mark the occasion such as Lorenzo Amoruso, Andy Goram and John Grieg, yet the task at hand was not forgotten.
In the 58th minute Rangers got their breakthrough - Barrie McKay worked the ball well down the left wing, and got to the byline to pull back for Templeton to turn home from six yards.
The home side were looking to build on their lead but Stirling went close to an equaliser with 10 minutes remaining - a catalogue of mistakes from the hosts' back line let in Josh Flood, but he could only find the inside of the post, with the ball being cleared.
That miss proved fatal as five minutes later McSorley saw red for a second booking, and Little made it 2-0 to the hosts after more fine work from McKay on the wing, who broke into the box before laying it off to the striker to apply the finishing touch.