Ponty scored five tries to two with young hooker Liam Belcher going over twice in a three-minute spell though Aberavon had three players yellow-carded and were down to 13 men for eight minutes.
Aberavon had led 10-8 after an amazing first-half try when wing Stefan Andrews ran to halfway and sent teenage full back Morgan Williams racing clear.
Aberavon head coach Jason Hyatt said: “We lost it in a 15-minute period in the second half as we made several errors, but I would like to see the penalty count.”
Pontypridd coach Geraint Lewis said: “Aberavon came out firing but after the interval we upped the tempo and it was particularly good to see our young players playing so well.”
Pontypridd led with a fourth-minute try by full back Matthew Nuthall, but after Nic Damjanovic and Simon Humberstone exchanged penalties came the Williams try, converted by Damjanovic, Another Humberstone took Ponty to the break and then came the two Belcher tries, one converted by Humberstone.
Referee Simon Rees sent Aberavon reeling with penalties, two more cards and a penalty try with Humberstone converting and then scrum half Lloyd Williams added the fifth Pontypridd try.
Aberavon finished with replacements Chris Morgans (try) and Ceiron Thomas (conversion) taking their tally to 17.
