The Welsh All Blacks have struggled so far this season but there was encouragement to take from their performance at The Park.
Quins moved into a 3-0 lead thanks to a penalty from fly half Craig Evans and after Neath had come close to a couple of tries, James Thomas levelled things up from the tee.
Evans' second penalty ensured a 6-3 interval lead and two more kicks from the summer signing pushed the home side nine points clear.
And when Neath prop Roy Jones was yellow carded, Quins struck to seal the win. Ellis Phillips crossed with Evans converting meaning Lee Evans' late try for Neath was irrelevant.
At Rodney Parade, Bedwas made it three consecutive away wins with a 20-31 victory over Newport.
Steve Law's side seem to be hitting form after a slow start but they were indebted to a Black and Ambers side who squandered a 17-9 lead. Nonetheless, the efficient visitors were deserved winners.
Newport had actually moved into an early lead, Elliot Frewen crossing after a searing break from young fly half Ethan Davies. Full back Geraint O'Driscoll converted and exchanged penalties with Bedwas' Richard Powell.
Newport were threatening to pull away but with mistakes creeping into their game, a number of good opportunities went begging. And when home lock Adam Frampton was yellow carded, Powell's second penalty made it 10-6 at the break.
Powell added his third penalty at the start of the second half but Newport hit straight back with a try from centre Dan Robinson. O'Driscoll kicked the extras and at 17-9, Sven Cronk's men should have secured victory.
But when James Thomas barged over and Glen Lewis raced into the corner, Bedwas had turned things around. Powell converted both scores and Ryan Evans completed the victory late on.