In the first match of the double-header, 16 points from Leigh Halfpenny, eight from Rhys Patchell, which included the opening try, and a second from Alex Cuthbert did the damage.
And Blues director of rugby Davies couldn't get enough of the performance of his players, although he made a point of saying that he wouldn't be getting carried away with himself.
"From one to 15, I thought we were magnificent. It's a big win for us because of the way we played. Glasgow are a tough side so it is pleasing to put together such a comprehensive performance together," he said.
"To play like we did for the majority of the first half and the desire we showed in the second half, although we were scruffy at times, was fantastic. It keeps us in the group which is terrific.
"It is a step forward for us and it keeps us in the group. We have a tough, tough game next week, but the pleasing think is they didn't get a bonus point.
"We have had two games in Europe at home against two quality teams and have acquitted ourselves well and got two good results. But there is a long way to go yet."
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