Glasgow started well but the same old failures returned to ruin their night. Handling errors, poor tackling and a lack of concentration led Glasgow to leak three soft tries in quick succession.
Glasgow dragged themselves back into the game with a great try from Glenn Metcalfe who was outstanding throughout. Borders struck back though with a try from ex-league man Gareth Morton but just before the break the Glasgow pack powered over with Andy Wilson getting the touchdown.
Warriors started the second half well but a misplaced pass from Gordon Bulloch saw Nikki Walker race in from his own half. A try by Nathan Ross, who was impressive in the loose, gave Glasgow some hope but three penalties from Tanner Vili put Borders out of sight.
Glasgow Coach Kiwi Searancke said: "Again we killed ourselves by making stupid and basic errors at crucial times. We handed them too much turnover ball and they made the most of it. They had some very good finishers and we played into their hands."