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 Welsh Rugby Union has announced a major new sponsorship deal with Gullivers Sports Travel which will make the UK's leading, and longest established, multi-sport tour operator, an Official Supplier for the rest of the decade.
Having taken part in seven World Cups as a player and coach, Liza Burgess hopes to go out in style this afternoon when Wales take on Australia in the Play-off for seventh and eighth place in the Women's Rugby World Cup in Paris.
WRU Head of Rugby Josh Lewsey met with volunteers across the game earlier this week, championing their role in the sport. He was joined by Wales captain Sam Warburton for part of the day as volunteers took part in a 'Try Out' event for the 2015 Rugby World Cup
Wales Women may not have got the results they wanted recently on the field, but off it they have made massive strides in strength and conditioning - and that is in no small part due to S&C coach Sam Dodge.
Two weeks into the new pitch project at Millennium Stadium, Groundman Craig Campbell takes staff on a unique behind-the-scene tour of the works so far and National Squad Assistant Strength and Conditioning Coach John Ashby and Tour Guide Peter Owen describe what the revamp means for them.
Try-scorer Jenny Davies and fellow prop Megan York reveal to WRU TV's Graeme Gillespie their thoughts after Wales broke their drought in the Women's Rugby World Cup with a 35-3 win over South Africa in Paris.
Wales Women are expecting a tough battle against South Africa on Saturday as both teams seek their first pool win of the Rugby Women's World Cup. WRU TV's Graeme Gillespie talks to head coach Rhys Edwards and lock Jenny Hawkins.
Wales' Sam Warburton took a group of employees from Admiral on a behind the scenes tour of the Millennium Stadium and WRU TV tagged along to bring you a snippet of what it's like for the players on match day