Tries from Chris Bowridge and Rhodri Milson put the game beyond Carmarthen after the break, before sin-bins for Dean Ronan and David Dyer saw Maesteg reduced to 13 men for 10 minutes in the closing stages.
A Maesteg spokesperson said: "I've never seen a refereeing performance like that in 30 years. But despite that, we produced an amazing display full of guts and courage."
Leaders Builth Wells fell to a shock 21-10 defeat against strugglers Penclawdd, and Mumbles came out on 18-16 winners in a thrilling game between the two bottom of the table rivals.
Aberystwyth continued their dominance at the top of Division Three West, running in six tries on their way to a 36-9 demolition of Tumble. Crymych were the other big scorers of the day, with a 33-0 win against Laugarne.
Aberavon Quins remain on top of Division Three South West after their 39-5 win against Briton Ferry. Second-placed Tondu are hot on their heels after scoring nine tries as they thrashed Seven Sisters 59-0.
Division Four West leaders Llandeilo are now red hot favourites for the title after a convincing 37-0 win over second-placed Tenby put them eight points clear at the top.
Bryncoch stay top of Division Four South West after they grabbed a 15-8 away win against Pontycymmer.
Cefneithin showed why they are top of the table with a massive 102-3 win over strugglers Swansea Uplands. The home side scored 16 tries in an emphatic display.
In the only game in Division Five South West, New Dock Stars beat Llandybic 24-22.