The two finalists were the most prolific try scorers in the annual tournament, in which 24 teams took part.
After getting a bye in the first round, Warriors overcame Currie, Ayr and Heriot's FP to reach the final.
Accies had beaten Kelso, Watsonians, Clermont Auvergne and hosts Melrose earlier in the tournament.
Glasgow squad
1 James Eddie
2 Finlay Gillies
3 Fraser Brown
4 Lee Jones
5 Scott Wight (Captain)
6 Mark Bennett
7 Carlin Isles
8 Folau Niua
9 Nikola Matawalu
10 Rory Hughes