The win however was marred by a serious injury to Reivers hooker Ross Ford who is now ruled out of Scotland’s surprise RBS 6 Nations Championship title bid.
The young Borders hooker – who starred in the closing stages of the historic triumph over world champions England at Murrayfield – was stretchered off after just two minutes of the crucial Celtic League clash at Firhill.
Ford suffered serious knee ligament damage as he landed awkwardly in a challenge and is likely to be sidelined until next season.
The home side carved out the first real scoring chance when centre Graeme Morrison swooped to intercept an intended chip over the top by Simon Danielli, but Andy Miller backtracked to halt the move with a brilliant tackle.
Immediately afterwards, Calum MacRae booted the Borders in front with a confidently struck penalty after Rory Lamont was guilty of playing the ball illegally on the ground.
Colin Gregor, who had been in such devastating kicking form in the Warriors’ stunning victory over league leaders Munster, squandered an opportunity to square the issue – and the visitors capitalised by opening up a 13-point advantage at the interval.
First, Danielli slid over in the corner for a tidy try in the wake of a scrummage on the 22-line.
MacRae banged over the tricky conversion – then added a penalty after Gregor had wasted another chance for Glasgow.
There was even more frustration for the home troops on the stroke of the break when skipper Jon Petrie was bundled out of play just a metre from the target after a powerful surge featuring Sam Pinder and Steve Swindall.
The Warriors had the better of the exchanges for the next 10-minute spell, but could not find a way through the watertight Reivers defence.
And their woes worsened when Miller galloped over for the second Reivers try after latching on to a pinpoint pass from fit-again stand-off Gregor Townsend. MacRae slotted the extra points from wide out.
Glasgow at least broke their duck when Gregor rediscovered his touch, but they were left with a mountain to climb even to salvage a consolation bonus point.
They gave themselves a glimmer of hope when Sam Pinder darted over following a quick tapped penalty under the crossbar by prop Kevin Tkachuk – but Gregor’s jitters returned as he sent the conversion wide.