The two semi-professional sides played out a 0-0 draw over 80 minutes at the Talbot Athletic Ground.
It was the first scoreless result in the competition so far this season.
The draw left third-placed Aberavon one point above bottom club Pontypridd in the four-team pool after two matches, and five points behind leaders Cardiff.
Highlights were few and far between in the Welsh Challenge Cup Pool B match between Aberavon and Pontypridd on Tuesday night.