The visitors raced into an early lead at Parc y Scarlets courtesy of a Moray Low try after seven minutes. Scotland International Ruaridh Jackson was off target with the conversion but kicked a penalty for his side two minutes after Rhys Priestland had kicked three points of his own.
Priestland then kicked two further penalties after 14 and 24 minutes respectively, the second edging the hosts in front for the first time.
Scarlets scrum-half Gareth Davies then touched down just before the break and Priestland was on target with the conversion to give his side an eight point cushion at the interval.
Half-time replacement Scott Wight kicked an early second-half penalty for the visitors and that was the only score until Wight kicked his second penalty with ten minutes to go, but the Scarlets hung on for their seventh victory.
