And in a nip-and-tuck encounter, a further try from the visitors - via wing Lee Williams - gave the Quins a 16-10 lead with just 10 minutes remaining. But if Llanelli do go on to win the title, they might look back on the last three minutes of this encounter as a crucial moment.
A try from wing Bowdy Davies, and an expert touchline conversion from Williams, gave the hosts a one-point lead, and, as Carmarthen pushed for a winning score, scrum half Justin James broke clear to confirm the win.
Aberavon stay just one point behind the leaders thanks to a 33-22 win at Bedwas. Tries from David Pritchard and Liam Gadd, as well as a penalty try, gave the Wizards their 18th win of the campaign. Jamie Davies added 18 points with the boot, but the visitors had to overcome a 16-13 half-time deficit as the second-bottom side gave the league challengers a scare.
Neath's outside hopes of finishing in top spot are over as they suffered a 39-26 home defeat to Bridgend at The Gnoll. The Welsh All Blacks endured a dreadful first half, and trailed 34-0 at the break thanks to tries from the Ravens' Lloyd Peers, Jamie Murphy (2) and Tom Habberfield.
A second half fightback gave the hosts a try-scoring bonus point, but a late Steve Cullen score for the visitors ended their resistance.
Elsewhere, Pontypool emerged on top in the battle of two lowly sides at Pontypool Park, triumphing 27-17 over Newport. Meanwhile, Tonmawr are still looking for their second win of the season after suffering a 45-0 defeat at Swansea.