But the Scarlets had to mount a comeback as the Dragons, who earned a losing bonus point, led at half-time thanks to two tries from Richard Fussell and then rallied at the end.
The Scarlets welcomed back Jones and Matthew Rees, as well as captain Simon Easterby, who were all rested for the 20-6 defeat at the Ospreys.
The Dragons handed a debut to former Nottingham prop Nigel Hall.
There was only one side in it in the opening exchanges as the Scarlets breezed into a 10-0 lead after nine minutes.
First Regan King showed his class by rounding two tackles to go over on seven minutes for a converted try before Stephen Jones planted a penalty goal.
A second try looked on the cards on 12 minutes but Jonathan Davies knocked on Mark Jones’ kick ahead into the Dragons’ 22.
But against the run of play the Dragons scored two converted tries through Fussell to take a 17-10 lead into the break.
First Fussell slid in at the left corner after Shaun Connor had set his backline going with a long pass, and he was over in the same corner again after good work by Jamie Ringer.
Connor made it 17 unanswered points for the Dragons with a penalty in the final minute of the half but he missed an easy penalty after the break which would have given the dragons a 10-point cushion.
After that the Scarlets began a concerted comeback, which was started with a Stephen Jones penalty and continued with a try for prop Phil John just before the hour mark as the home side went into a 20-17 lead.
That advantage was extended with three more Jones penalties on 60, 64 and 68 minutes But just when the Scarlets thought they had the match in the bag Connor converted his own try to cut the lead to 29-24.
But the Scarlets held on to secure the victory.
SCARLETS: Stoddart, Morris, King, Davies, M. Jones, S. Jones, Roberts, John, Rees, Manu, Day, Maling, Easterby, Edwards, Lyons. Replacements: Priestlend for Stoddart (74), Daniel for Morris (59), Reed for Maling (61), D. Jones for Edwards (75). Not Used: Cross, Schwalger, Cattle. Newport-Gwent D’gons: Tries: Fussell 2, Connor. Cons: Connor 3. Pens: Connor.
DRAGONS: Tovey, Wyatt, Sidey, Smith, Fussell, Connor, W. Evans, N. Hall, Willis, R. Thomas, A. Jones, MacDonald, Ringer, Charvis, L. Evans. Replacements: Isaacs for W. Evans (71), Black for N. Hall (55), S. Jones for Willis (55), Lydiatt for Ringer (69). Not Used: A. Hall, Maule, Dolman. Att: 7,050
Referee: James Jones (WRFU).