The Scarlets claimed first blood after some excellent work from their pack. Scrum half Dwayne Peel chipped ahead, and winger Dafydd James extended his Cup try-scoring record by powering over the top of three defenders for his 28th score.
The home side should have gone 10-0 up when they earned a penalty in front of the posts. Peel opted to run instead of giving the ball to Stephen Jones to slot between the posts, and the decision didn't look too wise when his pass to James went to the touch judge instead.
A blatant late tackle on Jones from Jerry Flannery should have resulted in a yellow card for the Munster hooker, but referee Chris White opted for only a penalty. Not many at Stradey Park have forgotten White's decision to blow up the Wales-Italy Six Nations match a bit "early", and let the Englishman know it.
Munster general Ronan O'Gara kept the Scarlets on the back foot with some clever touch-finders, but the Irish line-out, missing Paul O'Connell, couldn't take advantage.
With the line-out struggling, and Ireland's Test tighthead prop John Hayes being found out by the Scarlets' front row, Munster's grasp on the Heineken Cup was beginning to slip.
O'Gara's kicking out of hand was impeccable, but two missed shots at goal proved costly. The Scarlets' super-boot Davies slotted a long-range goal on to and over the crossbar and a try to flanker Gavin Thomas (with a hint of a double movement) in the final move of the half gave the home side a daunting 17-0 lead at the break.
Scarlets winger Mark Jones opened the second half by skinning opposite number John Kelly to score what looked like the match-clinching try, only to be called back for a forward pass. Referee White further endeared himself to the crowd in the next phase of play by overruling his touch judge's opinion and not giving the Scarlets a penalty when the same player looked to have been taken out without the ball.
O'Gara started showing the strain and had to be cautioned by White for swearing, but he made sure the Irish province troubled the scorers with a penalty goal from point-blank range on the hour mark.
Things looked grimmer for home fans when replacement lock Inoke Afeaki was yellow-carded two minutes after coming on to the field, and it was game on when Dowling scored in the corner, courtesy of a forward pass from All Black legend Christian Cullen.
The score, unconverted by O'Gara, made it a nine point ball game with as many minutes left on the clock, but a superbly executed try finished off by Davies settled the match. Scarlets and Wales back rower Alix Popham produced a bone-shattering tackle on Munster flanker David Wallace, and some classy work from Stephen Jones, Peel and centre Regan King gave Davies a score that brought the biggest cheer of the night.
A consolation try to Munster replacement Donnacha O'Ryan was barely noticed as West Wales celebrated.
Llanelli Scarlets 24 - 15 Munster
Llanelli Scarlets: Tries: G Thomas, D James, B Davies. Cons: S Jones (3). Pen: B Davies
Munster: Tries: I Dowling, D Ryan. Con: R O'Gara. Pen: R O'Gara
Llanelli Scarlets: B Davies; D James, R King, G Evans, M Jones; S Jones, D Peel; I Thomas, M Rees, D Manu, V Cooper, S MacLeod, S Easterby (C), G Thomas, A Popham (D Jones 75)
Replacements used: D Jones
Munster: C Cullen; J Kelly, L Mafi, T Halstead, I Dowling (T O'Leary 75); R O'Gara (C), P Stringer; M Horan, J Flannery, J Hayes, D O'Callaghan, M O'Driscoll (D Ryan 78), A Quinlan, D Wallace, D Leamy
Replacements used: D Ryan, T O'Leary
Yellow cards: I Afeaki (64)
Man of the match: A Popham (Llanelli Scarlets)
Referee: Chris White (England)