An impeccable kicking display from Stephen Jones helped Scarlets to a 22-12 victory on his 300th appearance for the side.
Jones kicked five penalties and converted Rhys Thomas' try on the stroke of half-time as the Scarlets extended their unbeaten run in all competitions to eight games, matching the record set in the 2002/03 season.
Jones was first on the board but the early lead was short-lived, with Jason Tovey responding from the tee.
Good hands released Dragons wing Aled Brew down the left hand touch, but a splendid cover-tackle from Gareth Maule prevented the first try of the evening.
Jones nudged Scarlets in front again on 18 minutes, and two minutes later his break down the centre of the field resulted in a Dragons infringement at the breakdown, which the fly-half duly punished to make it 9-3 to the home side.
Tovey again reduced the arrears and it looked like the Dragons would be going into the break within touching distance of their hosts until tighthead Thomas burrowed over from close range after new signing Viliami Iongi, on as a replacement for Maule, was hauled down just short of the line.
Tovey got the first points after the break with another penalty but the Dragons, who dominated possession, found themselves up against it when number eight Tom Brown was yellow-carded for more ill-discipline at the breakdown.
Jones struck two penalties during that period to one from Steffan Jones, who was just short with a last-minute effort from halfway that, had it gone over, would have seen the Dragons leave with a losing bonus point.
Pens: Jones 5
Pens: Tovey 3, Jones
Scarlets: 15 Daniel Evans, 14 Nick Reynolds, 13 Adam Warren, 12 Gareth Maule, 11 Sean Lamont, 10 Stephen Jones (c), 9 Gareth Davies, 8 Ben Morgan, 7 Johnathan Edwards, 6 Aaron Shingler, 5 Damian Welch, 4 Sione Timani, 3 Rhys Thomas, 2 Ken Owens, 1 Phil John.
Replacements: 16 Emyr Phillips, 17 Iestyn Thomas, 18 Deacon Manu, 19 Lou Reed, 20 Mat Gilbert, 21 Rhodri Williams, 22 Dan Newton, 23 Viliami Iongi.
Newport Gwent Dragons: 15 Martyn Thomas, 14 Tonderai Chavhanga, 13 Adam Hughes, 12 Ashley Smith (c), 11 Aled Brew, 10 Jason Tovey, 9 Wayne Evans, 8 Tom Brown, 7 Gavin Thomas, 6 Andrew Coombs, 5 Rob Sidoli, 4 Adam Jones, 3 Dan Way, 2 Rhys Buckley, 1 Phil Price.
Replacements: 16 Steve Jones, 17 Nathan Williams, 18 Nathan Buck, 19 Scott Morgan, 20 Jevon Groves, 21 Joe Bedford, 22 Lewis Robling, 23 Steffan Jones.
Referee: Leighton Hodges (Wales)