Trailing Stirling by 22 points after half an hour, the men from Meggetland battled back with a great second-half performance only to see the victory snatched away deep into added time thanks to a penalty try.
Stirling hooker Reyner Kennedy opened the scoring in the fourth minute, though Jonny Hope was off target with the extras.
Andrew Grant-Suttie crossed the visitors’ line, Hope again awry with the boot, before Ross Jones scampered in, Hope finally finding the target with the conversion.
Matt Donaldson then touched down for an unconverted try.
Craig Keddie raised Boroughmuir hopes of a renaissance when he finished off a good forwards drive late in the half, though Dougie Steele also missed with the conversion effort, and Robert Cairns notched a try ten minutes after the interval, Steele converting.
Hope stretched County’s lead with a penalty soon after, but back came the visitors again, capitalising on a yellow card for Stirling’s Mike MacDonald, Aaron Purewal finding space in the corner.
Robert Cairns brought Muir tantalisingly close with his second try, Steele converting, and they had a chance to take the lead with eight minutes left but Steele missed a straightforward penalty.
The comeback appeared complete when Dale Robertson barged over, Steel on target again, only for referee Graeme Wells to award that penalty try, which Hope gleefully converted for the win.