Centre Ford also helped himself to a try as did lock Lawrence Reynolds, after 23 minutes of the first half, and prop Rob Evans.
The Dragons crossed for a first half try from No.8 Gareth Evans but they tired in the second half as the Scarlets completed a deserved victory.
High Performance Manager Darryl Hill said, "It's all in the melting pot and will almost certainly go down to the wire. We have two games left and although much will be dependent upon other results, we are obviously looking to win both of those matches to keep ourselves in with a chance."
Dragons Team Manager Wayne Pugh said, "We competed well in the first half and at 5-5 at half-time, we felt we had a chance.
"Unfortunately, as the game wore on they came at us and finished strongly with 10 points in the last 10 minutes."