Scarlets book home quarterfinal
Leading just 7-3 at half time, thanks to a Ryan Elias score, Scarlets powered away in the second half to score the bonus point they required to secure home advantage in the next round.
Scarlets twice turned down kicks to the posts in the opening five minutes to go for the corner.
And it paid dividends in the sixth minute as hooker Elias went over in the left corner from a fine lineout drive.
After some confusion over the grounding the referee's initial decision to award the try was upheld and Leigh Halfpenny converted from close to the touchline.
But despite the early Scarlets dominance, Dragons reduced their deficit with 15 minutes of the first period to play as Arwel Robson knocked over a routine penalty.
Rhys Patchell then picked his way through the opposition back line but was just brought down with the line at his mercy as Dragons fought not to concede any more before the break.
But try as they might it looked as though they could not stop Scarlets as swift passing from right to left sent Halfpenny comfortably in at the corner – only for the score to be ruled out after the TMO adjudged Gareth Davies had knocked on at the base of the ruck before switching play.
And Scarlets were thwarted again as Joe Davies came in with a try-saving tackle with the clock in the red to deny Patchell what looked like a certain try.
After plenty of collapsed scrums in the first half Dragons hooker Dan Suter was replaced by Christian Coleman early in the second – only for another series of collapses, with Scarlets under the posts, leading to Coleman being sent to the bin, and one more collapse giving Scarlets a penalty try.
The floodgates then creaked open as Beirne finished off a move started by a break from Steven Cummins – Halfpenny striking the conversion against the post.
And the lock got a second, and Scarlets' all-important fourth, before the hour mark after stealing a Dragons lineout and crashing over when running onto the pass from the recycled ball – Halfpenny adding the extras.
But Dragons got a consolation in the 63rd minute as Jared Rosser dove over in the corner and the score was given despite a lengthy review by the TMO, who finally adjudged the winger successfully grounded the ball – Robson hooking the conversion attempt to the left of the uprights.
There was still time for Scarlets to score a fifth, though, as the Dragons failed to hold Steff Evans down and the winger got back to his feet to find a way through the defence from ten yards out – Halfpenny converting with five minutes to go.
All of which cemented a 33-8 win to set up a home quarter-final against Cheetahs next weekend.
Tries:Elias, Penalty try, Beirne 2, S Evans
Cons: Halfpenny 3
Dragons: 15 Hallam Amos, 14 Ashton Hewitt, 13 Zane Kirchner, 12 Connor Edwards, 11 Jared Rosser, 10 Arwel Rosbon, 9 Charlie Davies, 8 James Benjamin, 7 Aaron Wainwright, 6 Harri Keddie, 5 Rynard Landman, 4 Joe Davies, 3 Lloyd Fairbrother, 2 Elliot Dee (captain), 1 Thomas Davies.
Replacements: 16 Liam Belcher, 17 Luke Garrett, 18 Dan Suter, 19 Max Williams, 20 Taine Basham, 21 Sarel Pretorius, 22 Adam Warren, 23 Joe Goodchild.
Scarlets: 15 Leigh Halfpenny, 14 Ioan Nicholas, 13 Scott Williams (captain), 12 Hadleigh Parkes, 11 Steff Evans, 10 Rhys Patchell, 9 Gareth Davies, 8 Will Boyde, 7 James Davies, 6 Tadhg Beirne, 5 Steve Cummins, 4 Lewis Rawlins, 3 Samson Lee, 2 Ryan Elias, 1 Rob Evans.
Replacements: 16 Ken Owens, 17 Phil Price, 18 Werner Kruger, 19 David Bulbring, 20 John Barclay, 21 Jonathan Evans, 22 Dan Jones, 23 Steff Hughes.
Referee: Lloyd Linton (Scotland)
Assistant referees: Adam Jones (Wales), Gwyn Morris (Wales)
TMO: Leo Colgan (Ireland)