A scorching first-half hat-trick from Mark Jones left the Dragons floundering as the league's bottom Welsh region.
Scarlets (24) 36
Tries: M Jones (3), D James (2), Byrne
Cons: C Thomas (2), Hercus
Dragons (3) 17
Tries: Brew, Forster
Cons: A Thomas (2)
The Wales wing got three spectacular tries in the first half hour, Dragons unable to answer the home side's pace.
Jones' Wales and Scarlets wing partner Dafydd James added a brace of tries and another fell to full-back Lee Byrne.
The visitors did not threaten until the game was beyond them, scores coming to Nathan Brew and Jason Forster as the home side relaxed at Stradey Park.
The Dragons had named what many saw as a second-string team, targeting forthcoming games with Glasgow and Borders.
If they can finish above one of those sides plus bottom Irish province Connacht they can qualify for the Heineken Cup through a play-off with an Italian team.
Turnover ball cost the Newport side dear after 14 minutes, Matthew Watkins quickly firing out a long pass to Jones.
The Wales star beat Jamie Ringer easily, and when Leigh Hinton showed him the outside he quickly seized it to sprint in for an outstanding 65m strike.
A Matthew Rees run paved the way for the second score, Watkins putting in a wide cross-field kick from the recycled ball.
The bounce fell fortunately into the hands of Iestyn Thomas, the prop sending Jones clear in the corner.
Brew got a consolation try for the Dragons
The Dragons knew what was coming but had no answer as more loose ball on half-way was spun to Jones, who out-paced the cover defence of James Ireland to complete a 28-minute hat-trick.
The visitors responded with a Hinton penalty, but when Brew lost attacking ball it was the turn of James to profit.
He went for the line from 65m and had the pace to beat the unfortunate Hinton for the bonus-point score.
The stunned Dragons were given some hope before the break when Rees was sin-binned.
But the Llanelli side's forwards exerted all the pressure at the start of the second period, and when they finally released it across the back line Byrne had the pace to cross in the corner.
James was sent in unopposed for his second score after smooth passing along the three-quarter line.
As the Scarlets stepped back, Brew found a gap in the defence to register a
try for the Dragons.
From the restart, the Gwent side attacked from 60m and good handling saw replacement Forster canter in under the posts.
Scarlets wing Mark Jones:
"I'm fortunate to be in a team that suits my style and wants to spin the ball.
"It's been a barren few weeks, but the ball came my way today.
"We've had some decent performances but poor results lately and it was important to win against a committed Dragons side.
"The games are coming thick and fast now, but we know the task ahead and we want a strong league finish."
Dragons club captain Jason Forster:
"The turnovers were crucial - you can't do that at any level, let alone against players of the calibre of Mark Jones.
"It's been a difficult week for us - we've got ourselves into a hole and now it's up to us to get out of it.
"We have three huge games against the Scottish regions to come and have to dig deep.
"We know we have the ability but will have to do our utmost to get the results."
Scarlets: Byrne, D. James, Watkins, King, M. Jones, C. Thomas, Stuart-Smith, I. Thomas, Rees, Dunlea, A. Jones, Wyatt, Afeaki, D. Jones, A. Popham.
Replacements: G. Evans for Byrne (63), Gravelle for Watkins (69), Hercus for C. Thomas (40), L. Davies for Stuart-Smith (64), John for I. Thomas (60), Edwards for A. Jones (64), Mills for A. Popham (12).
Dragons: Hinton, Wyatt, Brew, Bryant, Breeze, A. Thomas, Ireland, Maddocks, Brown, Robinson, Griffiths, Sidoli, Oakley, Ringer, Owen.
Replacements: Chapman for Hinton (63), Black for Maddocks (65), Anthony for Robinson (54), Forster for Ringer (40), Hall for Owen (54). Not Used: Sweeney, Baber.
Referee: Nigel Whitehouse (WRU).