Penalties from opposing outside halves Neil Jenkins and Gareth Bowen got the scoreboard moving before Warriors wing Gareth Wyatt crossed for the first try after a quick throw-in close to the Scarlets line.
Bowen kicked two further penalties to one by Jenkins before Scarlets full-back Barry Davies squeezed over in injury time after Corry Harris had been sin-binned.
That score took Llanelli into a 16-13 interval lead and with Harris still in the sin-bin, the Scarlets increased their lead in the 43rd minute.
The Scarlets pack took advantage of Harris's absence to set up a try for John Davies from a line-out close to the line.
Two penalties from Jenkins closed the gap in the Scarlets favour to 21-19.
Jenkins and Bowen continued their kicking duel with the Llanelli man putting over another two penalties to one from Jenkins to keep the Scarlets unbeaten record intact.
Attendance 4,875
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