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 Warren Gatland and captain Sam Warburton say their first prioirty on Sunday in the opening game of the World Cup is to win against Uruguay and not get overly concerned with points difference.
With only days to go until the biggest rugby competition in the world begins, rugby fans visiting Cardiff this autumn will be able to enjoy a special display at National Museum Cardiff as part of the celebrations surrounding the Rugby World Cup.
Geraint John has taken up the new role of WRU elite coach development manager having arrived in Wales last week. WRU TV caught up with him at the WRU rugby department's strategy day at the Millennium Stadium.
The entire Welsh Rugby Union Rugby Department gathered at the Millennium Stadium earlier this week where WRU Head of Rugby Josh Lewsey looked back on a year where structural and strategic changes have seen significant progress made
The Welsh Rugby Union has released a specially produced video to spearhead a new campaign to help promote the values of rugby union. The video, entitled Let us Play underpins the WRU rugby department's philosophy - to engage, transfer and retain players, coaches and referees.