Steven Hampshire scored his first of the afternoon after just four minutes when Stirling failed to clear a corner. Shortly afterwards, Brechin got their second when Graham Gibson flicked on a Hampshire cross and David White was at the back-post to finish the move.
Hampshire then got his second to make it 3-0.
Brechin's lead was trimmed, however, when Paul Di Giacomo broke through their defence and fired the ball into the bottom corner to give his side a glimmer of hope. The striker capitalised on an error by James Sharp, who should have cleared the ball to safety.
In the second half Stirling came out fighting and got themselves to within one goal of the league leaders. Chris Aitken fired an excellent shot into the top corner in the 52nd minute after some more shabby defending from Brechin.
However, Brechin responded with two quick goals. Gibson worked hard down the right wing to cross a ball into Charlie King, who blasted the ball home. Gibson was in the box minutes later to slot away an easy chance.
Stirling scored a consolation goal in the 69th minute when Brechin substitute Craig Winter brought down Robert Dunn in the box, who fired home the resulting penalty. The remaining 20 minutes saw Brechin play out time and do enough to secure the three points.