The Scarlets led 5-15 at the break with tries by centre Naomi Thomas and prop Catrin Edwards with Evans's boot adding the extras. The Dragons only reply came from impressive flanker Jamie Kift.
The inspirational skipper Kift set the example and rallied her troops with a try in the second half but the Scarlets struck back through Evans.
The home side refused to buckle with prop Hannah Roberts powering over the try-line before Elen Evans scored the Scarlets final try in the dying stages. However the Dragons had the last say when Leila Johns scored.
For the Scarlets scrum half Jess Kavanagh and second row Kath Gravell stood out while backrower Sioned Harries was voted the Scarlets player of the tournament.
In the other game the Blues claimed a comfortable 33-10 victory over the Ospreys.
Becky Newton, Laura Prosser, Kiri Bennett and Levi Hallett scored the Blues tries with Prosser adding four conversions while in reply Amy Lawrence and Rachel Taylor touched down.