The Black and Ambers are now 32 games unbeaten at their historic ground having avoided defeat in the last two Welsh Premiership seasons. But they had to come from behind to beat a spirited All Whites side who led for more than an hour through tries from full-back Aaron Mitchell and flanker Ben Lewis.
However Swansea failed to shake off the home side, who stayed in touch with tries from Will Kershaw-Naylor and Alex Walker. The game finally turned Newport's way when outside-half Aled Thomas, one of Newport's new recruits this summer, gave the Black and Ambers the lead seven minutes from time. Centre Richard Payne went over late on to seal the victory.
Defending champions Neath crashed to their first defeat of the season at Sardis Road where Pontypridd clung on for a 25-21 victory. Neath looked dead and buried before Gareth Morris stormed over in injury time to bring them back to within a point only for James Hook to scuff his conversion. Instead Ponty outside-half David Flanagan held his nerve to slot over a penalty deep into extra time.
Llanelli's Lee Byrne scored two first-half tries as the Scarlets brushed past Ebbw Vale 24-3 at Stradey Park.
Cardiff's poor start to the season continued with a 42-20 defeat at Aberavon, having lost 49-8 at Ebbw Vale last week.
Premiership newboys Maesteg are still looking for their first victory since returning to the top division this season after two tries from Michael Wilcox and 19 points from the boot of Andrew James handed Bedwas a 29-10 win.
Bridgend full-back Gareth David bagged a 27-point haul that included a try in either half as the Ravens ran out 37-29 winners over newly promoted Glamorgan Wanderers.
Former Wales full-back Justin Thomas played a staring role with 18 points as Cross Keys ran riot against Llandovery, running in six tries in their 43-0 rout. There was no such free-scoring at Carmarthen Quins who squeezed out a 6-3 win over Pontypool.
Nearly 40 players were involved in the first Wales Under 18 training session of the season. WRU National Performance Manager Gethin Watts is excited at the potential shown by the group and expects the Regional Under 18 Championship to hone their skills even further.