Outside half Jamie Davies's goalkicking has played a major part in Aberavon's history and he took his club tally to 4,000 points in 13 seasons with conversions of both Matthew Jenkins touchdowns and three second half penalties.
Neath looked to be home and dry after sweeping into a 24-5 interval lead against Bargoed but the Championship side rallied after the break before eventually going down 39-27.
Neath outside half Dai Langdon brushed aside tacklers to cross in the opening minute and with Bargoed reduced to 14 men, further tries were scored by Gareth Gravell and Bowdy Davies to put the Welsh All Blacks 24-0 ahead.
Second half tries from prop Roy Jones and wing Chris Morgans settled the tie although Bargoed kept going until the final whistle.
Aberavon have been losing finalists on three occasions, 1974, 1975 and 2011 while Neath, who won the very first cup competition in 1972, have won the trophy on no less than six occasions.
The sides met on Boxing Day in the league last year with Neath winning 22-7 and the return fixture at the Gnoll is scheduled for this weekend with the winners being installed as favourites to make the final.
Carmarthen Quins are looking to reach their second final in three years after missing out to Llanelli in 2010.
Out to prevent that happening will be either Ebbw Vale or Pontypridd who still have to play their quarter final match.
Quins comfortably defeated Championship side Blackwood 32-14 to reach the semi-finals in a game postponed for 24 hours due to the inclement weather conditions.
They were ahead early on thanks to a try from hooker Richard Wilkes and kicks by outside half Jack Maynard and although Blackwood came back into the game, Quins extended their lead with touchdowns by Sean Bennett and full back James Dixon.
Further tries in the second period from Rheon James and Haydn Pugh sealed the Quins victory but to their credit, Blackwood never gave up.
Ebbw Vale have never reached a cup final but to earn the chance to appear at the Millennium Stadium this season they will have to knock out last season's runner-up, Pontypridd.
Ponty won the competition in 2011 and were winners in 1996, 2002, and 2006, and providing they can brush aside the Steelmen, they will be installed as favourites due to their position at the top of the league table.
Ties to be played weekend of April 13
Carmarthen Quins v Ebbw Vale or Pontypridd
Neath v Aberavon