The first half was a real war of attrition, Howard Packman and Steffan Evans exchanging converted tries with further opportunities limited to a pair of long range potshots from Will Hooley into the breeze.
But with Saints upping the intensity after the break and emptying a strong bench, the hosts had no answer - replacements Lee Dickson and Calum Clark adding tries two and three to kill off the game.
It was a game of relatively few moments of excitement, though the Saints’ opening score was one as Tom Stephenson split the line and exchanged a pair of passes with Packman who slid in for his second try in two weeks.
Having seen the visitors take their only clear cut chance of the half, Scarlets followed suit and Evans was on the end of an overlap to level things up 12 minutes later.
A swirling wind and on and off rain made things difficult for both sides, but when the Saints simplified things in the second half the forwards took a grip of the tie.
Both scores came following lineout drives, Dickson sniping over on the hour with advantage being played and Clark following suit just seven minutes later to make the game all but safe.
There was to be no bonus point, despite a couple of forays into the Scarlets 22, but Saints and Packman would still provide the game’s final highlight.
Having picked off a loose pass, substitute Aaron Warren looked home and hosed for a consolation try. Packman had other ideas, however, chasing the 60 metres back with the fresh-legged Scarlet and dragging him into touch to end the tie.
10mins SAINTS Try Packman Con Hooley 0-7
20mins SAINTS Miss pen Hooley
22mins SCARLETS Try Evans Con Shingler 7-7
33mins SAINTS Miss pen Hooley
HALF-TIME SCARLETS 7 SAINTS 7
49mins SAINTS Pen Hooley 7-10
60mins SAINTS Try Dickson Con Hooley 7-17
67mins SAINTS Try Clark Con Hooley 7-24
FULL-TIME SCARLETS 7 SAINTS 24