Gomer-Davies replaces Swansea's Gareth Swales, who has been rested.
Scrum-half Alyn Lake takes over from Ricky Richards (rib injury), a fit-again Kieran Crawford takes over from T R Thomas at hooker, and there has also been a change to the back row.
Cardiff's James Malpas is suspended for two games following his dismissal against South Africa, which means Ioan Cunnigham comes in on the blindside and Mark Lewis reverts to No 8.
'We wanted a top four finish, but that has gone from our grasp,' Wales coach Chris Davey said.
'Now we need to concentrate on finishing fifth. That means beating England and probably France on Sunday, who are favourites to beat Scotland.
'We are capable of doing that and even though we lost 50-21 to South Africa, we have taken a lot of positives out of that game. We have isolated seven errors that cost us the match. Other than that, we totally dominated the match and it was the kind of performance that we have been looking for from this side.
'If we can repeat the level of intensity and game building we showed against the young Springboks, then there is no reason why we can't beat England and France again.'
Wales Under-21: Rhodri Gomer-Davies (Llandovery); Jonny Vaughton (Swansea), David Bishop (Bridgend), Scott Williams (Newport), Matthew Nutthall (Pontypridd); Nicky Robinson (Cardiff), Alyn Lake (Bridgend); Paul James (Neath, captain), Kieran Crawford (Ebbw Vale), Rhys Thomas (Newport), Bryn Griffiths (Llanelli), Luke Charteris (Newport), Ioan Cunnigham (Llanelli), Robin Sowden-Taylor (Cardiff), Mark Lewis (Pontypridd).
Replacements: TR Thomas (Newport), David Maddocks (Llanelli), Chris Stamatakis (Cardiff), James Merriman (Gloucester), Darren Pittard (Swansea), Michael Hook (Newport), Nathan Brew (Newport)