Calvin Howarth weighed in with a try and three penalties and skipper Cammy Mather went over for a try to send Glasgow into the next round of the Celtic Cup.
Glasgow put late withdrawals and injuries behind them to record a rare away victory over one of the stronger Welsh regional squads. Glasgow lock Andy Hall was man of the match but there were also an outstanding performance from wing Sean Lamont. Glasgow's scrum and lineout also saw a vast improvement from the display last week against Ulster..
Glasgow's second-round tie will be played on the weekend of 3-5 October. But their opponents will not be known until the draw is made on Sunday.