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 last five years have been an emotional rollercoaster on and off the pitch for RGC1404. Promotion to the Principality Premiership was the culmination of five years of hard work and investment in North Wales. WRU TV caught up with prop Joe Simpson, who was one of the first intake of WRU North Wales Academy players in 2010.
Ebbw Vale captain Damien Hudd picked up the biggest accolade of the night at the 11th Principality Premiership Awards Evening held at Principality Stadium, after leading his side to the title for the first time.
Wales assistant coach Robin McBryde is predicting a tough battle against England on Sunday despite the fact they may not be considered to be at full strength. Players will be out to impress Eddie Jones which makes England a dangerous proposition, he says.
Wales U20 captain Tom Phillips and performance psychologist Dr Rich Neil explain why spending three days at Monmouth RFC has further strengthened the togetherness of the squad ahead of the #WorldRugbyU20s