Wales pair Ken Owens and Liam Williams scored in either half while young fly-half Owen Williams kicked 19 points.
And the Scarlets defence – spearheaded by centre pair Scott Williams and Jonathan Davies – helped secure a vital win. Victory saw Scarlets leapfrog Ospreys into fourth place in the battle to qualify for the end of season shake-up.
The foundations were laid in the opening 16 minutes when Scarlets cantered into an early 13-0 lead thanks to Williams and Owens.
Two early breaks by Davies both lead to penalties that Williams stroked home before Owens started and finished the move that lead to Scarlets first try.
Owens raced onto Johnathan Edwards pass, Scarlets forwards were patient as they edged their way closer to the try line before Glasgow captain Al Kellock stepped out of position in defence and the hooker dived over from close range.
Williams converted and added a clever drop goal after another Scarlets attack stumbled to keep the scoreboard ticking over.
Two penalties by Ruaridh Jackson cut the Scarlets lead to 16-6 by half-time but Scarlets seized the initiative immediately after the break.
Williams was wide with a penalty but the fly-half was involved in the attack that led to the second try.
Again Davies proved the catalyst with his charge, Owen and Liam Williams exchanged passes before the full-back latched onto North’s inside pass for an impressive try.
Williams converted and swiftly added a penalty after Josh Strauss’ high tackle on Aled Davies.
The fly-half then booted a fourth penalty on the hour for what proved to be the final score after Gareth Davies was held up over the line in the final minute.
