Despite the hard earned victory, Neath's Director of Rugby Rowland Phillips insists his side will be underdogs when they face Llanelli in the SWALEC Cup final on May 9.
Although being current Cup and League holders and four times Principality Premiership champions, Philliips insists the Scarlets will hold the favourites tag at the Millennium Stadium in three weeks' time.
He said, "There are some new boys in the Neath side this season so it's a big achievement for them to get to the final for the first time. Llanelli are above us in the League at the moment and although we are current Cup holders, on Llanelli's current form, Neath will be underdogs for once.
"Swansea were a very physical challenge to us in the semi-final - we weren't anywhere near the pace in the first twenty minutes - and they kept going until final whistle so they were a tough nut to crack. But the boys stuck to the game plan which came good in the end.
"The league may be out of reach but at least we've got the Cup to play for now. We've still got to play Llanelli away from home in the league too which will make things interesting but the Cup will be a nice carrot at the end of the season."