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 TV were on hand at the launch of a major new commercial deal with WRU and Mercedes-Benz South Wales (part of the Sinclair Group), which sees the family company become an official supplier to the Welsh Rugby Union
On the back of the recent Women's Rugby World Cup, the WRU has launched a revitalised Women's and Girls domestic seasonal structure, and the future is looking bright.
Go to www.wru.co.uk/tryourgame for more information
Roger Lewis talks to WRU TV at the announcement of a new £60 million Rugby Services Agreement (RSA) which provides a new and positive contractual relationship between the WRU and its four Regions for the next six years has been agreed.
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.