The Drovers took full advantage of their second bite of the cherry after getting an unexpected chance when Pontypridd were expelled from the competition after fielding an ineligible player against Llandovery.
The Welsh All Blacks were expected to coast to the final but the Drovers took them down to the wire where back rowers Nio Aiono and Dean Fitzgerald impressed alongside front rowers Peter Edwards and Emyr Phillips.
The Drovers gave as good as they got and led 10-6 at the break but the experienced Neath side dug deep in the second spell to edge a thrilling encounter.
Gareth McCarthy and Cerith Rees traded penalties with the Neath pivot edging his side in front with his second success. But the Drovers stung the home side with an excellent try after winger George North caught Rees's chip on the fly and raced clear.
Neath then lost centre Steve Thomas to the sin bin but three minutes after the break both teams were reduced to 14-men when Lloyd Phillips saw yellow.
Nathan Brew shuffled his way over in the corner then Neil Edwards and Josh Turnbull departed the scene with yellow cards.
Alec Jenkins banged over a monster penalty but plucky Llandovery hit back with a Matthew Jacobs try to bring them within a point.
But McCarthy sealed the victory when he slammed the ball on the try-line for a converted try and despite a late rally by the Drovers Neath were the first side to qualify for the inaugural play-off final.