Ross Kavanagh doubled Stirling’s tally shortly before half-time. City had goalkeeper Calum Antell to thank for saving well from a Peter MacDonald free-kick midway through the second period.
Montrose sit second and are the only other unbeaten side in the league after earning a 1-0 win over Cowdenbeath at Links Park.
Sean Dillon’s powerful header in the 19th minute proved to be the winner for the home side.
At the other end, Bradley Smith was thwarted by the crossbar in the 76th minute as Montrose held on.
Peterhead remain third despite suffering their first setback of the season, a 3-1 reverse at Stenhousemuir.
Jamie Longworth teed up Mark McGuigan for the Warriors’ opener in the seventh minute only for Mason Robertson to head the Blue Toon level on the half-hour mark.
A close-range finish from Nathan Blockley in the 52nd minute restored Stenhousemuir’s lead which was subsequently added to by the instrumental Longworth.
Elgin City moved to sixth with their first win of the campaign, a 3-2 comeback success against Clyde. Goals from David Goodwillie and Jordan Stewart handed the Bully Wee a two-goal lead within half an hour. Jamie Reid pulled one back shortly before half-time and Chris McLeish equalised in the 67th minute. In the final minute, Clyde goalkeeper Blair Currie was ordered off for a foul on Brain Cameron who dispatched the resulting penalty.
Annan Athletic picked up their first points of the season in style, with a 5-1 thrashing of Berwick Rangers at Shielfield Park.
After Michael McKenna’s early opener for Berwick, Annan hit back with goals from from Steve Swinglehurst, Ryan Sinnamon, Peter Murphy, Aidan Smith and Blair Henderson.