Felipe Contepomi hit the post with the last kick of the game to deny Leinster a comeback draw at Stradey Park.
Scarlets (17) 20
Tries: Watkins, B Davies
Cons: Hercus (2)
Pens: B Davies, Hercus
Leinster (10) 18
Tries: D'Arcy, Hickie
Pens: Contepomi (2)
Gordon D'Arcy opened the scoring after just four minutes with a 50m strike, but he then gifted an interception try to the Scarlets' Matthew Watkins.
Regan King sparked a superb Scarlets attack, although Mark Jones' scoring pass to Barry Davies appeared forward.
That try seemed decisive until Denis Hickie's late strike gave Contepomi the final chance he so nearly converted.
The Llanelli crowd, keen to witness a showdown between two Celtic League high-flyers, had been stunned into silence after just four minutes as Leinster won turnover ruck ball in centre field.
A creative pass from Keith Gleeson in the back line freed D'Arcy who cantered home.
D'Arcy went from hero to villain, throwing a laboured pass that Watkins intercepted for the equalising try.
Then the Scarlets outdid the much-vaunted Leinster backs, King igniting a regal move with a break outside Contepomi.
King fed Lee Byrne, who passed to Jones, before the wing sent Davies in with a suspicious pass.
The Llanelli side remained on the attack for much of the first half, but Leinster frustrated a series of driving mauls on their line.
Davies - celebrating the signing of a new contract at Stradey - landed a monster 52m penalty as the break approached, but that was cancelled out by a Contepomi kick.
Contepomi and Mike Hercus exchanged further penalties as defences tightened after the break.
That was all either side could muster in a lacklustre closing 40 minutes, but as the game ran deep into overtime the Scarlets transgressed offside.
Leinster kicked to the corner where their driving line-out was held, but the ball was spread for substitute Hickie to cross wide out on the left.
The crowd held its breath as Contepomi made clean contact with the conversion, but the ball struck the post and stayed out.
Scarlets man-of-the-match Alix Popham:
"It was a tight match, although I felt we controlled most of the game and could have scored more.
"They came back at us strongly in the last 10 minutes and we were lucky to hold on."
Scarlets: Dunlea, Rees, Madden, Louw, A. Jones, D. Jones, Easterby, A. Popham, Peel, Hercus, Byrne, King, Watkins, M. Jones, B. Davies.
Replacements: J. Davies for Madden (72), Cooper for Louw (53), Stuart-Smith for Peel (74). Not Used: Hawkins, G. Thomas, Bowen, G. Evans.
Leinster: Corrigan, B. Blaney, Green, O'Kelly, Byrnes, Gleeson, Heaslip, Easterby, Contepomi, Lewis, D'Arcy, O'Driscoll, Horgan, Dempsey, Miller.
Replacements: D. Blaney for Green (20), Williams for Byrnes (60), O'Riordan for Easterby (60), Hickie for O'Driscoll (64), Jowitt for Miller (40). Not Used: Hepworth, McCormack.
Referee: David Changleng (SRU).