Penalties from Rhys Patchell and Leigh Halfpenny gave the Blues a 6-0 half-time lead at Scotstoun and Welsh full-back Halfpenny added another three-pointer in the second half.
The Warriors wasted good chances before Ryan Grant delivered a late try for the home side, which was converted, but Cardiff held on for a vital 9-7 victory which boosted their hopes in Pool 2 of the Heineken Cup.
But Davies believes it could be the catalyst for a run of good results in the league as well with games against the Ospreys and Newport Gwent Dragons upcoming.
"We've got a plan on the rugby side and hopefully we'll get better and better,” said Davies.
"We'll savour this and hopefully move on to the [Pro12] Christmas derbies in good form.
"To come here and get the result is magnificent for the players. They deserve every accolade they get.
"It wasn't pretty at times for sure but our defence again was resolute throughout.
"We're trying to be competitive and consistent, that's the key thing. There's a lot of work going in.
"These last couple of results have been fantastic and we're moving forward.”