Kenny Logan scored his first try on home turf as Glasgow kept Borders rooted to the bottom of the table.
Glasgow: (12) 36
Tries: Pinder, Logan
Pens: Howarth (8)
Borders: (8) 22
Tries: Scott, Berthinussen, Blair
Cons: Warnock 2
The former Scotland winger crashed over late on to add to a first-half score from scrum-half Sam Pinder and 26 points from the boot of Calvin Howarth.
Borders went over first through veteran hooker Steve Scott but trailed 12-8 at the break.
Despite tries from Ian Berthinussen and Mark Blair, Borders were hampered by a Wayne McEntee yellow card for offside.
Glasgow: Rory Lamont, Rory Kerr, David Millard, Gareth Maclure, Kenny Logan (captain), Calvin Howarth, Sam Pinder, Andrew Kelly, Scott Lawson, Euan Murray, Andy Hall, Dan Turner, Steve Swindall, Andrew Wilson, John Beattie.
Replacements: Yet to be named.
Borders: Gareth Morton, Nikki Walker, Calum MacRae, Charlie Hore, Iain Berthinussen, Alistair Warnock, Drew Moore, Kelly Brown, Andy Miller, Andy Rennick, Colin Stewart, Mark Blair, Geoff Cross, Steve Scott, Paul Thomson (Captain).
Replacements: Will Kay, Tom McGee, Matt Parr, Scott Newlands, Wayne McEntee, Johnny Weston, Joe Pattison.