Fly-half Byrne scored 13 points from the tee at the Aviva Stadium and James Lowe dotted down in both halves as the defending champions stretched their winning run to four matches.
A penalty try for Leinster opened the scoring and although Tadhg Beirne and CJ Stander went over in the first half and Alby Mathewson added another 14 minutes from time, the Conference B leaders were not to be denied another win.
The Scarlets occupy second spot behind the holders after edging out their derby rivals 20-17.
Rhys Patchell’s second half try and the boot of Leigh Halfpenny – who finished with 10 points – ensured Luke Morgan’s try was in vain.
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