Newport wing Craig Richards gained his side's only try - his 17th - but fly half Matthew Jones contributed 17 points to push Neath to within three points of the top.
Aberavon gained a sound 32-11 win over Pontypridd where veteran international forward Dale McIntosh suffered a bad leg injury near the close of the match. Carmarthen Quins stay fourth after a strong second-half display saw them beat Ebbw Vale 46-6.
Llandovery were the team of the day however, as they gained their highest Premier score, defeating Pontypool 50-3 with exciting young wing Ifan Evans from Aberystwyth scoring a try hat-trick.
Swansea gained a 37-18 verdict over Cross Keys with centre Chris Shelmardine again impressing and Cardiff fly half Gareth McCarthy scored 20 points in a 45-3 beating of Caerphilly. Bridgend fly haf Austen Howells also notched 20 points in a 25-20 win over Bedwas.