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The Scottish side outscored the visiting Welsh region by three tries to one in a display that will give them confidence for the coming competition.
However, the victory was made easier thanks to indiscipline from the Cardiff pack. Irish referee Dave McHugh handed yellow cards to Canadian flanker Dan Baugh and prop Ben Evans, and late in the game, he was left with no choice but to expel robust forward Craig Quinnell for a stamping offence.
The former Cardiff player returned back to the land of his fathers from English club Worcester in the summer, and marked his return to competitive action with a red card. Blues coach Dai Young will have to order his players to stick to the letter of the law, or this could prove to be a difficult first season for the newly formed region.
By contrast, Glasgow coach Hugh Campbell will have been pleased to see all three of their tries being scored by new signings.
Former Newcastle Falcons wing Gareth Maclure, ex-Auckland scrum-half Sam Pinder and former Glasgow Hawks prop Euan Murray all touched down.
Outside-half Calvin Howarth completed a full set of a conversion, drop-goal and penalty to round off the tally.
For Cardiff Blues, centre Nick MacLeod scored their only try of the night, while fly-half Nicky Robinson added two penalties and a conversion.