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.
Whenever Bedlinog tackle Penallta a massive fixure is guaranteed but this Sunday there will be even more emphasis placed on the two rivals when they contest the SSE Swalec Plate final at Principality Stadium.
Ahead of their SSE SWALEC Bowl Final clash with Taffs Well at Principality Stadium on Sunday, Burry Port share their #FABXV nomination with WRUTV in the search for Welsh rugby's greatest volunteers. Everyone can get involved by sending nominations via twitter to @WRU_Community using the hashtag #FABXV
Cardiff Blues prop Gethin Jenkins and Ospreys centre Ben John look ahead to the first game at Principality Stadium in Saturday's double header which is promising to be a special occasion for all Welsh fans.
Carmarthen Quins Director of Rugby Ian Jones and committee member Jeff Thomas along with Llandovery chairman Handel Davies look ahead to Sunday's SSE SWALEC Cup showdown where both teams are out to prove 'West is best'
SWALEC ambassador Shane WIlliams is looking forward to Sunday's Finals Day where the Cup, Bowl and Plate offers a great opportunity for players and teams to experience the magic of playing at Principality Stadium
Carmarthen Quins coach Richard Kelly believes it is an exciting time to be part of the Scarlets region as his side take on local rivals Llandovery in the SSE Swalec Cup final on Sunday, as WRU TV's Graeme Gillespie discovers
Scarlets long serving prop Phil John talks to WRU TV's Graeme Gillespie about Judgement Day IV and SSE Swalec Cup finals day. The last time Llandovery were in the cup final in 2007, the Drovers claimed the spoils with Phil playing a major role in the engine room.
Meet Aberdare coach Luke Thomas whose #FABXV nomination goes to super volunteer Daz with a whopping 10 things he does for the club each week, all except the ironing! You can also join in the search for Welsh rugby's greatest volunteers, by sending your nomination via twitter to @WRU_Community using the hashtag #FABXV
SSE Swalec Cup kings Pontypridd travelled to Swansea, fully expecting a return to their second home but Llandovery had other ideas as they also sought victory in the semi-final to earn the right to play the final at Principality Stadium