Cardiff have now secured seven wins on the trot against Neath but had to overcome a rearguard effort from the visitors. The home side led 13-3 at the break after taking full advantage of Gareth Gravell's incarceration in the sin bin.
But Neath hit back in the second half to lead 17-13 before Cardiff edged back in front in trying conditions.
Dean Ryan was on Davies's shoulder to score by the posts and with Davies's conversion, on top of his two earlier penalty goals against one from Thomas, gave his side that 10-point lead at the break.
A penalty try and a touchdown by prop Anthony Lott made spiced up the scoreline and with Davies and Thomas duelling with their boot to bang over two penalties apiece, the Neath star appeared to have the points for the Welsh All Blacks, but Davies had other ideas.