Fly-half Jason Tovey contributed 13 points from the boot, while flanker Lewis Evans and second row Adam Jones grabbed a try each.
And with a double header against Exeter next up for the Dragons in their European competition, Edwards believes his side are starting to hit their stride.
He said: "The pleasing thing is the balance is starting to come together.
"We have got good decision makers, our experienced players are leading and we've got a couple of good players [Luke Charteris and Dan Lydiate] to come back in.
"We're in a lot better shape now, that was a good performance against Perpignan, it was important we stepped it up against a good European team.
"It was a big confidence boost, in the first half it was important we improved our style and in the second half we showed a great attitude and desire.
"Exeter have done well and they have won some big, physical games. They are a similar style team to Perpignan and it'll be another great challenge for us.
"But there is nothing for us to fear, we are five points clear at the top of our group and we've got to take great heart from our victory over Perpignan."
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