George North continued his comeback on the wing for the Scarlets, who also had Wales squad members Josh Turnbull, Tavis Knoyle and Rhys Priestland on duty, but he had few chances to shine in attack.
The Scarlets, who were led by Gareth Maule for the first time, dominated the early exchanges and should have made more of their possession and territory. But too many mistakes and turn-overs contributed to their downfall and they were 10-3 adrift at the interval despite most of the rugby.
Leinster started the second half strongly and took a stranglehold on the game up front. That allowed Sexton to knock over three successive penalties to stretch the home lead to 16 points.
At that stage it looked as though the Scarlets could be on the end of a hiding, but they regathered themselves and hit back with a close range try from Wales prop Rhys Thomas. Priestland added a wide angled conversion and there was a glimmer of hope again.
But a yellow card to Maule for persistent offside gave Leinster the chance to launch a back row move off a scrum five metres out and Boss dummied his way through for a try which Sexton improved.
There was a consolation score for replacement wing Nick Reynolds two minutes from time, but defeat meant the Scarlets dropped to sixth place while Leinster marched up to second.