Sexton made it 14-0 with a 43rd-minute drop goal and the Scarlets didn't score their first points of the match until the 47th-minute - Rhys Priestland landing a penalty.
Back the Scarlets came however as Gareth Maule scored a try soon after and Priestland converted to trim the gap to four but two more Sexton penalties pulled Leinster clear.
Priestland secured a bonus point for the Scarlets with a late penalty as Leinster ran out 20-13 winners - and Schmidt praised his side's ability to shut out the Welsh region for so long.
He said: "We performed really well, we put in a really good defensive performance and to contain the sort of armoury the Scarlets can throw at you - we were delighted to keep them scoreless for so long.
"They had some really good moments of pressure but we managed to keep them off the line.
"We were frustrated that we could not get the one extra score after going 14-0 up to give us a buffer for their heads to drop, but fair play to the Scarlets they gave nothing up."
Meanwhile, there was to be no repeat performance of Connacht's historic win over Harlequins last year as a double from Danny Care secured a thrilling win for the Premiership side at the Sportsground.
Ben Botica notched an early penalty for Quins but Dave McSharry grabbed a try for Connacht before Dan Parks hit four penalties to two more for the Kiwi as the Irish province led 19-9 on 27 minutes.
But scrum-half Care struck twice in the space of seven minutes to hand Quins a 24-19 led at half-time.
Parks struck again soon after the break to trim the gap to two but Botica struck twice more with the boot and 17 scoreless minutes to finish the game saw Connacht miss out on a losing bonus point.
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