Glasgow took the lead after good work from Cammy Mather, Graeme Morrison, Rory Kerr and great hands from Gareth Maclure led to the former Newcastle man going over in the corner after only six minutes. Calvin Howarth and Nicky Robinson then exchanged kicks as Glasgow led 11-6 at halftime.
Glasgow surged back into attack after the restart to snatch a second try. Scrum-half Sam Pinder dashed in to charge down a Don van Vuuren clearance, scooped up the loose ball and plunged over. Howarth slotted the conversion from wide on the left to open up a 12-point cushion.
Good work from the Glasgow pack after a lineout saw Euan Murray muscle his way over the line to give Glasgow a comfortable cushion. Cardiff hit back with a try from Nick Macleod but the sending off of Craig Quinnell for stamping saw the Cardiff challenge fizzle out.
"We struggled to win quality ball," said Glasgow coach Hugh Campbell. "But that can be rectified. When we had qualify possession we looked like stretching Cardiff," he said in turning to positive aspects of the game. "The potential is tremendous. We responded to pressure. We defended well. It was a new squad coming together," he pointed out. "That group had played together for only 20 minutes at most."