Davies, son of Scarlets director of rugby Nigel, scored all the Welsh points in the first half, kicking two penalties early on and scoring a try and conversion just before the break to give his side a 13-10 interval lead.
England were strong in the second period but tries from flanker and man-of-the-match Daniel Thomas and left wing Jake Randell kept the young Dragons in the hunt despite a yellow card for replacement Tomos Owen 15 minutes into the half.
Wales showed good composure in gaining territory and getting themselves into a good position for Davies to slot the decisive goal. The game wasn't over and England continued to press hard but Simon Davies' side put in a huge defensive effort to see out the clock and continue their 100% record in this tournament, which they have held for the past two seasons.
Team manager Roy James said, "We are very proud of the boys. They were under a lot of pressure territorially and England scored some good tries."
In the other match, France beat Italy 48-8. James added, "We are looking forward to playing Italy on Tuesday which is no doubt a game the home side will be targeting, then we play France at the Stadio Flaminio next Saturday."
Wales' game against Italy has been moved from the Stadio Tre Fontane to the Rugby Capitolino ground, the venue of today's game (kick-off 1.30pm).