Dragons reached the LV= Cup semi-finals but only after an improved second-half display as Scarlets threatened an upset.
For 45 minutes, the injury-ravaged west Walians, with nothing to play for after Gloucester won their group on Saturday, proved tough opponents.
Lead by prop Phil John and including ex-Wales and Dragons tight-head Rhys Thomas, they had the upper hand at the scrummages, with the old faults that have plagued the Gwent team over the last two years, coming to the fore again.
It did not help that the home team made countless handling errors, making the game stop-start.
The Pool Two leaders took the advantage early on when outside-half Matthew Jones booted a simple 20-metre penalty.
Visiting full-back Dan Evans replied for the visitors with a huge 43-metre shot between the posts before Jones restored the home lead on the half-hour when presented with a ten-metre shot in front of the posts.
Matters were not helped for the Scarlets when John was caught at the bottom of a ruck with what seemed like a leg injury that saw him stretchered off.
Evans had the chance to level again when home skipper Tom Willis was seen to be stamping by the touch-judge but the penalty shaved the upright.
However, the Scarlets did managed to go into the break on equal terms when they drove into the home 22 and were rewarded with a penalty that Evans landed.
And the Scarlets took the lead for the first time after the interval when they came close to scoring the opening try, as Thomas lead the drives that took them towards the home line.
Dragons wing Aled Brew, though, gave the visitors another penalty that Evans gratefully received when he dived into a ruck offside.
Finally, the game began to improve and the Dragons grabbed the first try. It came from a powerful move into the 22 where wing Adam Hughes set-up a ruck.
Evans saw 6ft 7in second row Luke Charteris on the left wing, passed the ball and the ex-Wales lock just escaped an Aaron Shingler tackle to touch down in the corner.
Jones missed the conversion but kicked his third penalty that gave his side an eight-point swing to lead 14-9.
And, just after the hour, the Dragons pulled away as full-back Martyn Thomas, just back from an horrendous leg injury, crashed over twice in the left corner.
The first came when Jones fed centre Pat Leach to put the full-back in, with Jones adding a superb touchline conversion.
Then, with eight minutes of the game left, the Dragons drove the Scarlets eight back on their own line, setting-up numerous rucks until the ball was spun through replacement stand-off Jason Tovey for centre Pat Leach to swing a long pass out to the unmarked Thomas.
That was enough to finish matters off and send the Dragons through.
Tries: Charteris, Thomas 2
Pens: Jones 3
Pens: Evans 3
Dragons:15 Martyn Thomas, 14 Adam Hughes, 13 Matthew Watkins, 12 Pat Leach, 11 Aled Brew, 10 Matthew Jones, 9 Wayne Evans, 8 Joe Bearman, 7 Lewis Evans, 6 Andrew Coombs, 5 Rob Sidoli, 4 Luke Charteris, 3 Pat Palmer, 2 Tom Willis (C), 1 Hugh Gustafson,
Replacements:16 Lloyd Burns, 17 Scott Roberts, 18 Dan Way, 19 Scott Morgan, 20 Hugo Ellis, 21 Mike Petri, 22 Ashley Smith, 23 Jason Tovey.
Scarlets:15 Daniel Evans, 14 Darren Daniel, 13 Nick Reynolds, 12 Scott Williams, 11 Joe Ajuwa, 10 Owen Williams, 9 Gareth Davies, 8 Damian Welch. 7 Nic Cudd, 6 Aaron Shingler, 5 Nathan White, 4 Adam Powell, 3 Rhys Thomas, 2 Rhys Lawrence, 1 Phil John (c),
Replacements: 16 Craig Hawkins, 17 Sean Hopkins, 18 Dean Howells, 19 Duane Eager, 20 Mat Gilbert, 21 Martin Roberts, 22 Jonny Lewis, 23 Rheon James.
Venue: Rodney Parade
Referee: Greg Garner (England)