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.
Welsh players and management joined Deputy Minister for Sport Ken Skates at the Pierhead Building, Cardiff Bay earlier this week to reveal the Union's pioneering school-club hub initiative has been so successful the project will now almost double the scale of the original project.
The Scarlets, Newport Gwent Dragons, Cardiff Blues and the Ospreys look ahead to Judgement Day III which sees the Blues take on the Ospreys (2.30) and the Dragons tackle the Scarlets (4.45pm) at the Millennium Stadium tomorrow afternoon.
Ystradgynlais and Ynysddu played out a titanic struggle at Taffs Well in the SSE SWALEC Bowl semi-final. At the end of the game neither team could be separated after a 15-15 stalemate but Ystradgynlais go through on try count.
Blues strike first in JD III battle - Newport Gwent Dragons lock Andrew Coombs, WRU referee Dylan Llyr Jones and Cardiff Blues hooker Matthew Rees decide dressing room allocations for Judgement Day III
Wales Under 18 captain Calum Haggett has received a conditional offer to read Biomedical Science at St Anne's College, Oxford. WRU chairman Gareth Davies went to meet Calum and Coleg y Cymoedd Principal Judith Evans to wish him luck in his exams and pass on some of his personal experience.
Dodgy tattoos, carthorses, Avatar and soft chins are revealed by Wales Sevens players Tom Williams and Sam Cross as they profile the Wales Sevens squad taking part in Hong Kong this weekend in the latest round of the HSBC Sevens World Series.