The 23-16 victory at St Helen's saw Aberavon reach the semi-finals of the competition as they aim to go one better than their cup final defeat in 2011 at the hands of Pontypridd.
"Being an Aberavon boy, I'm so proud to have done it [reached 4,000 points]," said Davies
"It's an honour to play for the club and be the record point's scorer.
"I feel extremely proud. I'm glad to get it out of the way to be honest - it's been a bit of a countdown really since I've come close to it."
Carmarthen Quins, Neath and either Ebbw Vale or Pontypridd will join Aberavon in the hat for the semi-final draw.