County took the lead at Meggetland through a Jonny Hope penalty before Muir skipper Chris Laidlaw booted a reply for 3-3.
First try of the game went to County, when Ruaridh Leishman went over in the 16th minute and Hope converted.
However, Laidlaw grabbed a converted try to make it 10-10 before County took the lead with a second try six minutes before the break, pack pressure telling when Alex Taylor powered over.
Another penalty from Laidlaw just before half-time left Boroughmuir 13-15 down – but straight from the kick-off the home side went ahead. County spilt the ball and Matthew Tweddle scored a converted try.
Both sides scored penalties before Dougie Hearn added a cracking try for Boroughmuir.
Adam Nicol grabbed one back for County before a Jordan Edmunds try sealed the win for the hosts.
Hope kicked a late penalty for a losing bonus point.