Geraint O'Driscoll also booted 16 points as 'Pooler' recovered from the loss of prop Nicky Blake, who broke his leg in the second half.
But Ospreys youngster Kristian Phillips and Gareth King both scored twice to save the blushes of last season's double-winners in front of their home crowd.
"We expected it to be difficult and Pontypool didn't disappoint us," said Neath coach Rowland Phillips.
"We were playing against a team we didn't really know much about and we didn't play well enough. It simpy wasn't good enough as far as our standards are concerned.
"We have been successful int he past, but as far as I'm concerend all of that is in the past. We have to build moving forward."
Despite the loss of British Police prop Blake, who is likely to miss much of the rest of the season, Pontypool coach Gareth Lintern was bullish about the start his side made back in the big time.
"We had been looking forward to this game ever since last season. It was a superb performance and we are bitterly disappointed we didn't win it," said Lintern.
Aberavon made the perfect start to the new campaign with a 29-27 victory over local rivals Swansea at St Helen's.
Ian Moore, Dai Pritchard, Richard Morris and Luke Hatherway all went over to clinch a bonus-point victory for the Wizards despite a late recovery by the All Whites.
Richard Kelly crossed twice to clinch two consolation points for Swansea's losing margin and scoring four tries.
Scarlets outside-half Rhys Priestland was on target as Llanelli beat Glamorgan Wanderers 24-13 at Stradey Park. Adam Powell, Daniel Evans and Ian Jones all scored while Priestland kicked seven points.
Ebbw Vale have finished in the Premiership's top four for the past two seasons but were held to a surprise 6-6 by Bedwas.
Dai Langdon and Andrew Williams both converted penalties for the Steelmen but Phil Dollman struck twice to share the points at Eugene Cross Park.
Rory Pritchard and Carl Hocking grabbed tries as Bridgend won 20-8 at Llandovery who saw prop Craig Cross sent off a minute after coming on as a replacement early in the second half.