Fullback Jack Evans was the star for the Scarlets, contributing 17 points.
On a dry but breezy evening, the Scarlets played into the wind in the first half although it mattered for little as they soon opened up an advantage.
From the start, the Scarlets combined error free rugby with great composure both with and without the ball as they ran out convincing 32-0 winners.
It took just seven minutes for the home side to open the scoring, prop Richard Bassett crashing over after the Scarlets forwards had given them territory inside the opposition half.
Evans converted and then added a try of his own. From a scrum near the halfway line, the Scarlets' backs moved the ball wide with the fullback using his pace to cross under the posts.
The Dragons battled hard but could not match the Scarlets' enthusiasm to play running rugby and further scores from Billy McBryde and Kieran Jones added gloss to an easy win.