The victory was built on a solid forward platform, the Swansea scrum showing just what they are capable of in front of the S4C television cameras.
Wales Under 20 internationals Nicky Thomas and Nicky Smith were at the heart of the front row effort with Wales No. 8 Dan Baker producing a barnstorming display from the back of the scrum.
After a disappointing season last year, the result was a real boost for the All Whites, their pack earning a penalty try with a second score arriving from the outstanding Baker.
Neath's quest for victory wasn't helped by seeing three men yellow carded. But that was more down to Swansea's forward dominance than any Neath deficiency, the home side's early penalties from Adam Jones left as a distant memory.
IRB Junior World Player of the Year Sam Davies had replied for Swansea and with Smith and Thomas destroying the Neath set piece, it wasn't long before flanker Garyn Daniel and prop Ceri Jones were yellow carded for the home side.
A penalty try inevitably followed, with Davies' conversion and a second penalty putting Swansea 13-6 to the good.
Swansea were dominant but Neath replied on the stroke of half time, Dai Langdon finding Liam Davies with a superb cross kick.
With Neath trailing 13-11 at half-time, Jones and Davies exchanged penalties at the start of the second period.
Swansea's second try soon arrived though and when it came, there was no surprise as to its source. Another monstrous scrum saw Neath prop Mark Jones yellow carded, allowing Baker to touch down.
Gareth Bateman replied for Neath with a late converted try but it was their old rivals who were deserved winners.