Stephen Jones led by example for the hosts on his 300th appearance as the Scarlets condemned their Welsh rivals to their sixth defeat of the season.
Jones and his opposite number Jason Tovey exchanged penalties in the opening five minutes.
Jones then put the Scarlets in command with two further penalties after the Dragons failed to make the most of their territory and possession.
Tovey grabbed a penalty back for the visitors, but former Dragons prop Rhys Thomas crashed over just before the break to extend his side’s lead.
The Dragons fly-half kicked his third penalty at the start of the second period but that was soon cancelled out by another three points from the boot of Jones.
Replacement fly-half Steffen Jones looked to have grabbed the Dragons a losing bonus point with a late penalty, but that was cancelled out by his namesake Stephen.
