Newton had the chance to kick off the Scarlets' 5000th game celebrations on 13 minutes with a penalty, only for him to fluff his lines.
But the fly-half made amends five minutes later, only for Fijian Nacewa to level with one of his own on 21 minutes.
The hosts tried as they might to give their home fans something to cheer about but came up against a strong Leinster defence.
Nacewa seemed desperate to spoil the party, kicking his second penalty a minute before the break to give Leinster a slender three-point lead going into the second half.
And the full-back was at it again just two minutes after the restart to double the Irish side's advantage.
But Scarlets retook the lead five minutes later, scrum-half Ruki Tipuna getting the move flowing by breaking through three tackles before feeding Johnathan Edwards who found Williams who crossed the whitewash, Newton converting for a one-point lead.
However that was as good as it got for Scarlets as moments later Rob McCusker was sin-binned, Nacewa slotting his fourth penalty.
On 54 minutes Nacewa kicked his fifth penalty and that was it for the scoring, Newton first spurning the chance to reduce the arrears with a kick of his own on 67 minutes before the Fijian was wayward with five minutes to go.
|Scarlets Score Card|
|Leinster Rugby Score Card|