The Blue Toon made sure of the points in the 64th minute as Stirling were caught on the break, Russell McLean teeing up talismanic forward Rory McAllister for his customary goal.
In close pursuit of the leaders, Annan Athletic trail Peterhead by only one goal after a comprehensive 3-0 success at Berwick Rangers.
Aidan Smith gave Annan the ideal start as he pounced to score with a sublime lob after a long clearance had been shambolically dealt with.
On the hour mark, Annan doubled their advantage when the free-scoring Tommy Muir headed home a Tony Wallace cross after which there was to be no way back for beleaguered Berwick.
Indeed it got worse for the Northumberland side when David Wilson’s top-corner finish in stoppage time added a third for impressive Annan.
Edinburgh City climbed to third with their third win in four league games in the form of a 2-0 triumph at stumbling Clyde.
The home side’s Kevin Nicoll and Chris McStay both went close in an opening period that Clyde had the better of.
However, just after the hour mark, City took a surprise lead when Blair Henderson found Scott Shepherd who made no mistake from six yards.
The capital side soon added a second when Graham Taylor fed Henderson to continue a prolific start to the season.
Queen’s Park rose to the top half of the table courtesy of a simple 2-0 win against bottom side Albion Rovers, who are yet to score a league goal or earn a league point.
First-half goals from Kurtis Roberts and William Mortimer were sufficient for the Spiders, for whom Scott Gibson missed a 50th minute penalty in the wake of Rovers’ Barry Eley’s dismissal.