The Blacks got off to positive start when scrum half Gareth James to claim a fourth-minute try. Fly-half Thomas converted and landed a 40-metre penalty, but opposite number James Dixon then hit a post with a simple penalty. However, he soon made amends, slotting over two close-range penalties that kept the fired-up Old Parish in the frame.
A wet ball led to countless errors, and Neath were unable to find the rhythm that has made them such a force this season. The Blacks only held a 10-6 advantage at the break, but early in the second half a rumble from the forwards set up a corner try for wing Aled Brew.
A touchline conversion from Thomas was followed by a penalty as Neath eased into a 20-6 lead approaching the hour mark, and they were home and dry once assistant coach Patrick Horgan touched down from a first touch in the 70th minute.
Maesteg will have to find a way to breach the Neath defence as the two sides perpare for their Konica Minolta Cup semi-final next Sunday. That match will be played at the Talbot Athletic Ground, and shown live on S4C. (kick off 17:10).
Tickets are available directly from the clubs. Meanwhile Cardiff - who play Pontypridd at Rodney Parade in the other Konica Minolta Cup semi-final on Friday evening (19:10) - lost out to Swansea 19-27.
The visitors completed the double over city rivals Cardiff at a rain hit St. Helen's. However, the win came at a cost as the Whites lost four key players to injury during the 80 minutes. Four well taken tries from Richie Rees, Tim Evans, Jonny Vaughton, and Leigh Bevan were enough to deny a spirited Cardiff side. Tickets are available from the clubs, and also from Rodney Parade.