But it was another case of the home side's ill-discipline costing them the game.
Coach Neil Edwards will want to get to grips with these issues before next Friday's trip to neighbours Swansea, which only a few short seasons ago, was a match between the top two in the Premiership grand final.
Newport got the better of the opening exchanges and, after a couple of penalties pushed them into the Neath half, the visitors claimed a lineout inside the Neath half.
The ball was worked into the backs, before a sweet inside ball put Poole into space from five metres out .
He crossed with ease and Scott Sneddon added the conversion for a 7-0 lead for the visitors.
There followed a period of play that summed up Neath's season, several opportunities for breaks but handling errors or ill-discipline at the ruck area scuppering scoring chances.
Neath did finally get on the board in a busy period of injury time. Dai Langdon landed three penalties on 40, 42 and 43 minutes and the Blacks had an unlikely lead of 9-7 at half time.
After the break, Newport came back firing and within 10 minutes had retaken the lead, following hands on the floor, via Sneddon's boot.
The former Cardiff and Wanderers man added another penalty on 53 minutes, this time for not rolling away, and the visitors had a 13-9 lead.
Frustration grew for the Neath faithful on the hour after referee Perkins binned Captain Lee Evans for what he deemed persistent infringement.
Newport carried on regardless and even a change of kicker couldn't throw them off kilter, as Geraint O'Driscoll took over where Sneddon had left off, adding a further penalties on 63 and 72 to confirm the victory at 19-9.
There was a sense of frustration at full time that, even though Newport deserved the win, this was one that got away for Neath.