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.
WRU International Skills Coach Jason Strange is a busy man, combining the new role with that of Wales Under 20 attack coach, Ebbw Vale head coach and continuing to teach at Ebbw Fawr Learning Community.
Warren Gatland and Sam Warburton look ahead to this week's crunch RBS 6 Nations tie against France, where the Wales skipper in particular is keen to make his mark, as Paris has proved a bleak place for him in the past.
Following their historic win over England, Wales Under 20 suffered a narrow, 36-34 loss to their Scottish counterparts last weekend, despite outscoring them by five tries to three. Watch the match highlights and reaction.
WRU TV go behind the scenes with the Wales squad as they put the final touches in place ahead of the clash against Scotland at Murrayfield. Follow the squad on their captain's run, the kickers visit to Murrayfield and Neil Jenkins' press conference