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.
As the countdown continues for RWC2015, Tournament Chief Executive Debbie Jevans visited the Millennium Stadium to discuss preparations for the eight matches and reveal the positive news that 100,000 tickets for games at the home of Welsh rugby have sold in the last seven days.
Jason Harries is targeting a first win on the World Series circuit this season with Wales. The series returns to action this weekend in Dubai where Harries is part of a team hoping to build from its efforts in round one in October.
Wales skipper Jevon Groves says his side have addressed a few points from Gold Coast and aim to 'hit the ground running' in the next two rounds of the World Series, kicking off with this weekend in Dubai before heading off to South Africa next week.
Wales Sevens manager Steff Thomas is hopeful his side can build from a quarter-final spot in the opening round of the World Series in Australia when his side take part in the forthcoming double header in Dubai and South Africa.