A drama filled night at Scotstoun Stadium saw Rhys Patchell and Leigh Halfpenny kick Blues into a 9-0 lead in a tense encounter with ten minutes left.
However, Blues were forced to dig deep throughout the clash to withstand Glasgow pressure and a grandstand finale was assured after Ryan Grant scored for the hosts late on.
A missed penalty from Duncan Weir with two minutes left resulted in Glasgow throwing everything at Blues in the closing seconds before the final whistle sparked scenes of visiting delight.
"We've had some big wins in the past the Blues, but in the context of this game, and considering who was out, that was magnificent from the players," said Davies.
"The desire and determination to try and play in the conditions was great. Our defence was resolute throughout and to come here and get the result is great for the players. They deserve whatever credit they get.
"We are all in it together and the last seven or eight weeks we have worked so hard. The opportunities have come for some players and they have taken them.
"The challenges have been there for all to see. We have had some tough games and we have become more consistent because of the way the boys are working. They are stepping up week in and week out.
"We have a lot of players to come back, which is pleasing, but these guys deserve everything."