The Cheesemen refused to lie down and tries by wing Gareth Holmes and replacement scrum half Andrew Peggington took them to victory.
Neath had to beat off a Pontypridd rally to secure their spot in the semis by 27-18 at the Gnoll. Fly half Matthew Jones scored 12 points and Gareth Morris gained the vital try after Neil Boobyer's try had put Pontypridd back into the game.
Ponty skipper Dale McIntosh knew his side might had missed an opportunity to cause an upset.
'We really, really felt that we could win the cup this year. This was the largest hurdle and if we got past this we were into the semis,' he said. 'But to come to Neath and get a result was going to be very, very hard.
'The final try was a real stake through the heart and it's a score we didn't really deserve to concede.
'We were very persistent and committed but to be fair to Neath they absorbed all our pressure and perhaps in the end that was a telling factor.'
Cross Keys and Aberavon will try again at Pandy Park on Sunday at 2.30pm, while there is no date yet or the Brynmawr-Bridgend tie.