Wales took the game to England in the opening ten minutes and were rewarded with the first points, Davies kicking over a penalty to put the hosts 3-0 up. But England hit straight back and a nice break from scrum half Callum Braley eventually freed up LV= Breakthrough Player of the Year winner Nowell to touch down in the corner.
With 17 gone Wales regained the lead, Davies' second penalty made it 6-5 before Slade had the chance to put England back into the lead, but saw his kick sail wide. Davies then slotted his third successful kick of the night with 25 gone to make it 9-5.
Slade brought England to within a point after 34 minutes, his first successful kick of the night, a penalty from just inside his own half. And as the half drew to a close England opted for touch instead of posts, a decision justified as back row Wells touched down for his first England try, converted by Slade. Wales were also reduced to 14 men with No. 8 Ieuan Jones sent to the sinbin for repeat offenses.
The hosts started the second period as they had the first, putting England under pressure, pressure that was eventually rewarded as Davies stroked over his fourth penalty but Slade hit straight back for England to make the score 18-12 with 54 played.
With the gap at six, both sides were giving it a real go, a Slade drop goal increased the gap to nine but Davies returned fire with his fifth penalty of the night to make it 21-15.
Wales pushed on knowing a converted try would win them the Championship, but it was England who had the final say. Slade again opting for touch with points on offer, but a strong driving maul was touched down by Wells for his second to give England the 28-15 win.
Departing Head Coach Rob Hunter said: "It's a massive achievement and the guys deserve all the credit - they're a hard working group and this trophy is their reward for the work that they have put in. Wales gave it a real go and full credit to them, we never felt comfortable."
Captain Jack Clifford added: "I'm so happy for all of the boys and all of the management, everyone works so hard and to end up with this trophy as captain is a dream come true. Massive credit to the Welsh though, at no point did we feel like the game was won until the final whistle blew."
England: Nowell 1T, Wells 2T; Slade 2P, 2C, 1DG
Wales: Davies 5P
England Under 20 starting XV to play Wales
15. Ollie Devoto (Bath Rugby)
14. Anthony Watson (London Irish)
13. Tom Stephenson (Northampton Saints)
12. Sam Hill (Exeter Chiefs)
11. Jack Nowell (Exeter Chiefs)
10. Henry Slade (Exeter Chiefs)
9. Callum Braley (Bristol Rugby)
1. Luke Cowan-Dickie (Exeter Chiefs)
2. Nathan Morris (London Wasps)
3. Kyle Sinckler (Harlequins)
4. Elliott Stooke (Gloucester Rugby)
5. Dominic Barrow (Leeds Carnegie)
6. Harry Wells (Leicester Tigers)
7. David Sisi (London Irish)
8. Jack Clifford (Harlequins)
16. Max Crumpton (Saracens)
17. Danny Hobbs-Awoyemi (Northampton Saints) on for Luke Cowan-Dickie 67 mins
18. Danny Herriott (Northampton Saints)
19. Tom Jubb (Saracens)
20. Gus Jones (London Wasps)
21. Alex Day (Northampton Saints)
22. Henry Purdy (Leicester Tigers)
23. Ben Howard (Worcester Warriors) on for Ollie Devoto 73 mins