Neath did cross the line three times through full-back Gareth King, fly-half David Langdon and back-row Adam Whitney, but it was not enough to stop the Welsh All-Blacks from suffering their fourth loss of the season.
Cardiff recorded a high-scoring derby victory over rivals Swansea, overcoming their indifferent form to beat the All-Whites 36-34 after trailing 17-3 at half time at St Helen's.
Centre Richard Smith scored a brace of tries, followed by flanker Rhys Shellard and scrum-half Rhys Dyer.
Smith's midfield partner Darren Ryan was the ultimate hero for the away side, storming over in injury time, allowing fly-half Joe Griffin to convert for the win.
Third-placed Aberavon destroyed basement-side Glamorgan Wanderers, with the Wizards touching down 11 times in a 75-19 triumph.
Wing Richard Carter and centre Ashley Beck both scored hat-tricks in the try-fest, with opposite wing Richard Thomas grabbing a brace.
The kickers also played their part, managing to convert 10 of the 11 tries - outside-half Matthew Jarvis hitting five and his replacement Jamie Davies add the same number.
Meanwhile, a penalty try and five Steffan Jones penalties helped Cross Keys secure a 22-10 victory over Pontypool, condemning Pooler to their 12th loss of the season.
Tonmawr came out on top in a mid-table clash with Bedwas at Bridge Field, winning 28-21 in a five-try game. Tries from Bedwas full-back Stuart Thomas and prop Scott Roberts were not enough to stop the Pitmen coming away with the win.
Newport eased past second-from-bottom Llandovery, with the game at Church Bank finishing 29-18. The Black and Ambers managed to secure a bonus point thanks to two tries from No8 Hugo Ellis, as well as touch-downs from wing Owen Broad and hooker Andrew Brown.