The visitors extended that lead with a well worked try by Chris Knight before Knight added a second within two minutes.
The home side were down to 14 and when space appeared, Knight was able to slide over in the corner. Cardiff's day got worse when a charge down led to Owen Evans adding the Drovers third to send the visitors in 33-3 up.
Cardiff's performance improved in the second-half but the damage was already done. Llandovery secured a bonus point through a Phil Day try, Lee Rees added a fifth before outstanding back row forward Richard Brooks got the reward his work deserved when he scored Llandovery's sixth.
Cardiff did manage three tries in the second half, Reuben Tucker scored under the posts following a Thomas Young break with the second try the result of persistent pressure.
Adam Williams pounced on a loose ball to put Matt Smith in before Tucker got his second as he went over from short range.
Griffin converted two of the tries, but it wasn't enough for the Blue and Blacks to get anything out of the game.