An early goal from Liam Warman earned Barry all three points at Richmond Park, with the visitors continuing their excellent away form in Carmarthen.
Callum Sainty burst through the Carmarthen midfield, feeding Warman on the right. His well-struck shot was too hot for the ‘keeper to hold, giving Barry a 4th minute lead.
Both Kayne McLaggon and Aiden Lewis saw chances flash by the Carmarthen goal, but it remained 1-0 at the break.
The home side pushed forward in the second half, in search of an equaliser, but Barry’s defence was strong, Mike Lewis securing the first clean sheet of the competitive season.
Carmarthen ended the game with ten men when Tom Dyson was shown an injury time red card after a mis-timed challenge on Mikey George, and Barry holding out for the three points.