Burns had a hand in all three of Gloucester's tries, scored by Shane Monahan, Tom Savage and Shaun Knight, with his counter-attacking ability proving a constant threat to the Exiles defence.
He stepped up to get the Cherry and Whites out of the mire, having spent 10 minutes in the sin bin, after they had let an 18-6 lead slide to be trailing 25-24 with eight minutes left.
Seizing on turnover ball, Burns spotted the space to combine brilliantly with wing James Simpson-Daniel and pave the way for Knight's clinching try.
His role in Monahan's opener was equally impressive as he broke out of his own 22 before taking a quick tap penalty with the Welsh defence snoozing to allow the winger to get over.
Burns also contributed 13 points with the boot and with England's autumn campaign against Fiji, Australia, South Africa and New Zealand just over a month away, Davies believes Red Rose boss Stuart Lancaster needs to give serious consideration to selecting his fly-half.
He said: "I have worked with a lot international 10s and he is certainly up there that's for sure, and the fact he has been able to mature at this level for a couple of years has certainly helped him.
"As a 10 it's not all about you, it's about the team and how you run the team and he is starting to do that for us now.
"He is playing exceptionally well, there is no doubt about it.
"A game like this can be very difficult for you if you don't get it right at number 10.
"But for large parts of the game he controlled the game, put us in the right areas and he was a constant threat.
"His goal-kicking is improving all the time and his out of hand game management and kicking is excellent at the moment too, so he is really maturing."
Welsh had been able to keep themselves in the game through the boot of Gordon Ross, who kicked 20 points, and prop Franck Montanella's score looked to have given them a third straight win, until Burns turned the game decisively in Gloucester's favour.
Exiles coach Lyn Jones admitted his players were frustrated.
"We didn't kick well in the first half, and that brought Gloucester into the game," he said.
"As a result they managed to score two good tries, so turning round 18-9 down with couple of bad injuries, you are up against it.
"We showed some spirit and came back, we managed the game well and got our noses in front, but we had a penalty advantage before the break in front of the posts that went begging and there was one with 15 minutes to go that we failed to deal with.
"We had our opportunities but it wasn't to be today. You have to deal with ups and downs of the season but I think the boys are frustrated and disappointed as it was within our grasp but we need to learn how to play accurately."
Jones also confirmed the first-half injuries suffered by hooker Neil Briggs and centre Sonny Parker appear serious.
"Sonny has gone for an x-ray on his ankle, it could be ligaments, it could be a fracture, we don't know, we will have to wait for the results on that, and Briggs had a nasty traumatic situation with his shoulder," he said.
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