Glasgow broke their Celtic League duck by edging out the Borders in a jittery encounter at a gusty Greenyards.
Broders (7) 7
Glasgow (10) 10
Former Glasgow winger Stuart Moffat put Borders ahead with a first-half try, with Charlie Hore extending the lead with the successful conversion.
But skipper Paul Thomson was sin-binned and scrum-half Sam Pinder went over the line for Glasgow, with Dan Parks levelling the scores with the boot.
A Parks penalty soon put Glasgow ahead and they survived late pressure to win.
Borders (7) 7. Tries: Moffat. Cons: Hore. Glasgow (10) 10. Tries: Pinder. Cons: Parks. Pens: Parks. Att: 2,500
Borders had made a storming start by creating a series of raids that pinned Glasgow back in their own danger zone.
Their efforts were eventually rewarded when Moffat timed his angled run to perfection as he latched on to a clever inside pop-pass from hooker Stevie Scott and brushed off Jon Petrie's challenge to reach the target.
Hore slotted the conversion, only for the Borders to suffer an immediate setback when Thomson was sent to the sinbin.
Glasgow took instant advantage of their extra player by squaring the contest.
They earned the feed by wheeling a scrum under the Borders crossbar, allowing Petrie to pick up the ball at the base and send scrum-half Sam Pinder scuttling past flanker Wayne McEntee for the touchdown.
Outside half Parks defied the swirling breeze to thump over the goal and followed up with a confidently-struck penalty to give the Warriors the edge at the interval.
Glasgow reappeared without Lions hooker Gordon Bulloch, who had taken a knock and he was replaced with Scotland Under-21 international Scott Lawson.
Borders soaked up early pressure and stepped up the tempo at the other end and Moffat looked on course for another score until he was bundled into touch just a metre short of the line.
They kept up the momentum and should have levelled the issue with a simple penalty by Hore, but he pulled it narrowly wide.
Glasgow were then left raging when they were denied what appeared to be a valid second try.
Paul Dearlove could not cleanly gather a Parks cross-kick and, after the ball dribbled backwards, full-back Scott Barrow scooped it up and plunged over.
But Welsh referee Hugh Watkins ruled that Dearlove had committed a knock-on.
The Borders' own frustrations were complete when Hore missed another penalty with the last kick of the game.
Borders: Morton, Steel, MacRae, Dickson, Moffat, Hore, Cusiter, Thomson, Scott, Douglas, MacLeod, Blair, Gray, McEntee, Rennick.
Replacements: Ford, Parr, Stewart, Cross, McKearchar, Millar, Warnock.
Glasgow: Barrow, Lamont, Morrison, Henderson, Logan, Parks, Pinder, Tckachuk, Bulloch, Harrison, Beardshaw, Ross, Wilson, MacFadyen, Petrie.
Replacements: Lawson, Kelly, Hall, Dearlove, Beveridge, Howarth, Craig.
Referee: Hugh Watkins (Wales)