The Scarlets scored the only try of the match at Parc y Scarlets - a second-half effort for wing Lee Williams.
However Leinster, who made three changes following their home defeat to Glasgow last week, played the better all-round rugby.
Leinster took a 6-3 lead into the break but the first half was a largely forgettable 40 minutes dominated by mistakes and the whistle of Irish referee John Lacey, who officiated the ruck area to the letter of the law.
It took 17 minutes to break the deadlock when Scarlets outside-half Dan Newton found the target with a penalty goal for an offside offence, five minutes after missing with his first attempt.
From one of the many ruck offences committed by the Scarlets, Nacewa put over his first penalty to lock the scores at 3-3 after 21 minutes.
Twice the Scarlets eventually got through some phases but twice - Ben Morgan and Gareth Maule - were blown up for holding on at a ruck.
A minute before the break Leinster put together a concerted attack with number eight Leo Auva'a at the heart of it. It forced the Scarlets offside, leaving Nacewa a relatively easy kick to give the Irish province the lead for the first time.
Nacewa sparked the game into life straight after half-time with a weaving run which produced a penalty kicked by the Leinster full-back to extend his side's lead to six points.
Newton missed a penalty five minutes later but suddenly from the 22 drop-out the Scarlets scored a try inspired by a run from scrum-half Ruki Tipuna, who linked with lock Aaron Shingler before wing Williams went in down the right. Newton converted.
New Zealander Tipuna was surprisingly taken off as the Scarlets made wholesale changes in the final 30 minutes.
But the Scarlets, who had flanker Rob McCusker sin-binned for a ruck offence, were only to hold their lead for four minutes as Nacewa kicked penalties after 51 and 54 minutes to give Leinster a five-point cushion.
And the home side, who have now lost three of their opening four Pro12 games, ran out of ideas, meaning man of the match Nacewa could afford to miss a penalty 13 minutes from time.
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