With scrum half Aled Davies having withdrawn, Llanelli brought in Jak Evans from the bench and in his first competitive start, he put in an excellent shift for his new club.
Josh Lewis opened the scoring with a penalty on four minutes before a well worked try from in-form hooker Kirby Myhill saw Anthony Buchanan's side extend their lead.
The Drovers soon replied and got on the score sheet after 20 minutes with a well struck James Garland penalty. Johnny Lewis then finished off a fantastic passage of play for a Llanelli score which, despite the season being in its infancy, will surely be a contender for try of the year.
Llandovery responded immediately with an excellent try from full back Mike Evans with Garland converting. It meant the half finished 13-10 to the visitors.
Strangely, the second half also ended 13-10 to Llanelli as they secured what was probably a deserved victory. They did put themselves under pressure though, replacement Nathan White yellow carded with 10 minutes to go.
The start of the second period had seen Llanelli score two penalties from Josh Lewis who also converted a penalty try. For the Drovers, Garland kicked another penalty and their captain Phil Day touched down in injury time - a score to which Ian Brooks added the extra two.
It was not enough though as Llanelli progressed to join Rotherham, Bedford and Connacht in Pool 3 of the British & Irish Cup.