As it was, Newport emerged with a 13-12 victory as they bounced back from their previous defeat to Bridgend.
The muted atmosphere did not lend itself to a classic but it was closely and keenly-fought throughout. Neath had the greater share of possession and territory but Newport scored the only try of the game through a first-half Owen Broad score that Geraint O'Driscoll converted.
That gave Newport the lead after Cummins had landed two penalties as a reward for some solid combined approach work by the visitors and, although Neath threatened, the nearest they came to scoring was a kick and chase by centre Lloyd Phillips.
Trailing 6-7 at half time, O'Driscoll and Cummins traded penalties and then repeated the act as the two teams strived for the ascendancy.
Neath came close to scoring off a short-range scrum but knocked on and, with Chris Morgans looking threatening and John Leyshon making inroads from centre, they stepped up the pressure.
When referee Gwyn Morris reversed a penalty outside the home 22, Cummins stepped up but missed his kick at goal and with replacement No.8 Lee Evans and his team throwing everything at the Newport line, he fluffed his second chance and with it went Neath's hopes .
Neath coach Patrick Horgan said, "It was one that got away. We had enough in us to win it and it was our own fault that we didn't. But again the boys gave it everything and the game really could have gone either way.
"We must make sure that we nail down opportunities like that in the future and will need to do so in our next match - at home to Bargoed in the Cup quarter final on Saturday week."