The Blues left Firhill empty handed after a disappointing night of rugby.
Cardiff Blues - minus their international contingent - were turned over at Firhill on Friday night in a 28-0 defeat.
Glasgow are now placed second on the Magners League table, inspiring coach Sean Lineen to say: "Second in the league might be a little foreign to us, but Glasgow is an exciting place to be right now.
"The guys could now either get a bit dizzy or just say, 'right, we're on to something special here'."
Tries from Mark McMillan, Max Evans (2) and Lome Fa'atau helped to the victory.
But the Blues, who are not enjoying the best of league campaigns, clearly missed Wales squad members Martyn Williams, Jamie Roberts, Tom Shanklin, Gethin Jenkins, Leigh Halfpenny and Andy Powell and injured former All Black Xavier Rush.
Their cause was not helped when instrumental fly half Nicky Robinson left the field injured after just 11 minutes.
With just 11 points from six games played, Dai Young's side face a race with the Dragons for automatic Heineken Cup qualification. The Blues are one point, and one place, ahead of the Gwent side, who have 10 points from six matches.
The British & Irish Cup kicks off this weekend with the four Regional Premiership Select XVs flying the flag for Wales. Welsh
Sat 14 Nov: Blues Premiership Select v Nottingham (2.30) & Connacht Eagles v Dragons (2.30)
Sun 15 Nov: Yorkshire Carnegie v Ospreys Premiership Select (1.30) & Scarlets v Bedford Blues (3.00)
The Welsh Rugby Union is forming a new Youth Board with a brief to help keep more young people involved in the game during their late teenage years and beyond. The first task of the fifteen strong Board will be to analyse and consider the issues which lead to a number of youngsters drifting away from the sport between the ages of 16 and 21. To apply visit www.wru.wales/youthboard
The Foster's Challenge Cup will involve the 12 Principality Premiership sides and will run during European and British & Irish Cup weeks, providing vital fixtures for the participating clubs and an opportunity for upcoming players to step up to semi-professional rugby and make a claim for starting places within the Premiership squads.
Eighty schools and colleges in Wales now have a full time rugby officer as part of the WRU's school club hub scheme. All of the school club hub officers recently gathered at the National Centre of Excellence for various workshops.
With Liam Williams forced out of the World Cup through injury, lock Luke Charteris and Skills Coach Neil Jenkins say they have to put yesterday's defeat behind them as Wales now look ahead to another physical encounter against South Africa in the quarter-finals of the Rugby World Cup.
WRU Consultant Head of Physical Performance Paul Stridgeon praises the Physical Performance department for their work and dedication as he addresses the media ahead of Wales' Pool A clash against Australia
Twelve young people have been selected to follow a one year WRU Coach Core apprenticeship programme. Coach Core was set up by the Royal Foundation of the Duke and Duchess of Cambridge and Prince Harry as part of the Olympics legacy in 2012 and the Duke of Cambridge was on hand to meet the apprentices on their first day in the job. The programme has been funded by the Hunter Foundation.