A long-range penalty from the Quins and yet another converted try from the Welsh All Blacks' Young brought the score to 33-33.
But it was a comeback that just wasn't to be. A last minute penalty for the Quins was confidently kicked home by fly half Craig Evans, making the final score 36-33 to the league leaders.
Elsewhere, Pontypridd secured a solid 35-20 victory over Llandovery, moving the Sardis Road club up to second position in the league while the Drovers are knocked down to third. Both sides gave a strong performance but in the end Ponty proved the tighter side, with three tries coming from Rhys Shellard, Geraint Walsh and Lloyd Williams and a penalty try awarded 55 minutes in.
Cardiff emerged victorious from their meeting with rivals Swansea, beating the All Whites 18-14 after a tight game and an underwhelming half time score of 7-7. Cardiff's tries were scored by Ryan Harford and Mike Stephens, but it was a well-placed penalty from Jack Maynard that secured victory for the Blue and Blacks.
In a stunning result Newport fans will remember for a long time, the Black and Ambers sealed a comprehensive win over Bridgend, thrashing the the Ravens 46-24 away from home. Both sides are currently languishing near the bottom of the league and this result could have repercussions for later in the season. The win sees Newport rise to eighth in the league, while Bridgend drop to tenth.
At the Talbot Athletic Ground, Aberavon scraped a 27-26 victory over Cross Keys with tries from Tom Duncan and John Phillips. Ceiron Thomas kicked 12 points for the Wizards to make it five wins on the bounce.
On Sunday, Llanelli defied a rain-lashed Parc y Scarlets to secure a 13-9 victory over Bedwas. Richard Powell kicked three penalties for Bedwas but it was the home side who came out on top. Llanelli had the dream start with an opportunist try from centre Gareth Owen that Josh Lewis converted. Bedwas came back into things but another Lewis penalty and three points from Dion Jones secured the win.
Principality Premiership results:
Aberavon 27 - 26 Cross Keys
Bridgend 24 - 46 Newport
Neath 33 - 36 Carmarthen Quins
Pontypridd 35 - 20 Llandovery
Swansea 14 - 18 Cardiff Rugby
Llanelli RFC 13 - 9 Bedwas