After a fractious start in wet conditions, Wales got the first points on the board through fly half Jack Maynard before England's No. 10 Burns levelled up two minutes later.
With 20 on the clock centre Pohe got England's first try - patient build up from the forwards eventually freed up the 17-year-old Leicester youngster, who showed a nice step before darting over the line.
England's second came five minutes later, a short line-out inside the Welsh 22 was well caught by Maro Itoje and the resulting rolling maul was touched down over the line by Moriarty to make the score 17-3.
Maynard reduced the deficit to 11 with his second penalty to draw the first half to a close with England 17-6 to the good.
Wales started the second half strongly and scored with 43 played through flanker and captain Ben Roach and Maynard's successful kick put Wales to within a try of the lead.
England could have extended their advantage when wing Josh Watkins made a nice break and found scrum half Callum Braley in space, but the Hartpury No. 9 was closed down quickly and his pass out wide to Zach Kibirige was knocked into touch.
Fortunately England's third try did come soon after, another short line-out was well gathered and prop Wilson forced the ball over the line to put England 22-13 up with 15 minutes left.
A Welsh penalty, again from Maynard, with five minutes to go brought them to within a converted try of the lead, but England's solid defence held firm to ensure their place in the final.
Fletcher was proud of his side after the game and said: "We're delighted with the effort and delighted with the result but we've still got some work to do. The game could have gone either way to be honest, they had a lot of the ball and they had opportunities to hurt us.
"It was a fairly even game but we'll move on from this and look to better ourselves in the final. Our forwards were excellent, our set-piece was very good and it provided the platform for the win."
Try scorer Moriarty added:
"I'm really happy to get the win both from a personal point of view and for the team. We worked really hard today, it might not have been the prettiest but we got the job done. I spoke to my dad [Paul Moriarty, former Wales player] after the match and he was chuffed - we just can't wait for the final now."
England Under 18 starting XV
15 Zach Kibirige (Yarm School) (Newcastle Falcons)
14 Josh Watkins (Bromsgrove School) (Worcester Warriors)
13 Tom Stephenson (Moulton College) (Northampton Saints)
12 Javiah Pohe (Wyggeston & Queen Elizabeth 1st) (Leicester Tigers)
11 Nathan Earle (Oaklands) (Saracens)
10 Billy Burns (Hartpury College) (Gloucester Rugby)
9 Callum Braley (Hartpury College) (Bristol Rugby)
1 Danny Hobbs-Awoyemi (Moulton College) (Northampton Saints)
2 Harry Thacker (Leicester Grammar) (Leicester Tigers)
3 Scott Wilson (Sedbergh School) (Newcastle Falcons)
4 Maro Itoje (Harrow School) (Saracens)
5 Charlie Ewels (Bryanston School) (Bath Rugby)
6 Ross Moriarty (Hartpury College) (Gloucester Rugby)
7 Gus Jones (c) (Eton College) (London Wasps)
8 Josh Buggea (Hartpury College) (Worcester Warriors)
16 Reece Marshall (Moulton College) (Northampton Saints)
17 Harry Rudkin (Wyggeston & Queen Elizabeth 1st) (Leicester Tigers) on for Danny Hobbs-Awoyemi
18 Alex Lundberg (Hampton) (London Wasps)
19 Jake Oldaker (Wellington College) (Bath Rugby) on for Maro Itoje
20 Joel Conlon (Ivybridge Community College) (Exeter Chiefs) on for Josh Buggea
21 Tom Chapman (Colfe's School) (Saracens)
22 Sam Olver (Oundle Schhol) (Northampton Saints) on for Billy Burns
23 George Catchpole (Leicester Grammar) (Leicester Tigers)
24 Nick Carpenter (Filton College) (Bristol Rugby)
25 Max Northcote-Green (Millfield) (Bath Rugby)
26 Howard Packman (Moulton College) (Northampton Saints)
Content courtesy of RFU.