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.
Wales Head Coach Rob Howley talks to WRU TV's Sebastian Barrett about the 36-man squad he has just named for the forthcoming Under Armour series, which includes two uncapped players, Ospreys duo Sam Davies and Rory Thornton.
Head coach Rowland Phillips is deligthed he can now call BT Sport Cardiff Arms Park home for his Wales Women's side, who launch their international season next month with games against Scotland and UK Armed Forces in the heart of the capital city.
Wales Sevens star Sam Cross has put his home town club of Brynmawr on the map after winning a silver medal at the Rio Olympics with Team GB. His club have now honoured him by naming their players bar after him, as WRU TV discovered at the official launch, recently.
One of the newest members of the Principality Premiership, Bargoed admit it's proving to be a steep learning curve at the highest level, but are determined to become a force to be reckoned with. WRU TV visited the club last weekend when they took on Llanelli.
Table-topping Aberavon travel to north Wales to tackle RGC 1404 as both teams defend unbeaten starts to the season in the Principality Premiership. WRU TV's Graeme Gillespie visited the Wizards to see how their preparations were going for the game of the weekend.
The Half a Game initiative is currently sweeping across Wales and proving a major success. The scheme aims to give every young player at least half a game every weekend. WRU TV recently visited a festival in Narberth where clubs have fully embraced the initiative.
Both Bargoed and Swansea were seeking their first win of the Principality Premiership season this afternoon. It proved a fruitful day for the hosts - not only did they win, but Bargoed claimed a try bonus point.
Cardiff managed to keep their unbeaten record at home intact, but only just as Bridgend made them work extremely hard before the Blue and Blacks secured a hard fought Principality Premiership win at the BT Sport Arms Park last night.
Former Wales back row Andy Powell gives a guided tour of The Wern, home of Merthyr RFC, who are determined to prove a lot of people wrong and make their mark in their first season in the Principality Premiership.