The Welsh side had led 27-0 after a sparkling opening salvo, but Leinster, without most of their Ireland stars, fought back strongly after the break.
Llanelli crossed for two tries inside the opening four minutes and had notched up their four-try bonus point with just over a quarter of the match gone.
With the sun beating down at Stradey Park, the Scarlets played some spectacular stuff early on to stun the Irish side, who had been delayed arriving at the ground because of traffic on the journey from their hotel.
The had only had one touch of the ball, a dropped kick-off by flanker Stephen Keogh, before watching the Scarlets touch down for their first try by Dafydd James.
Tongan second row Inoke Afeaki followed soon after following some superb handling involving forwards and back. James’ second score was all down to a slick three-quarter line with Kiwi centre Regan King making the initial break, feeding full-back Ceiron Thomas, who off-loaded just short of the line.
A Jones conversion and then penalty from straight in front made it 20-0 to the home side with barely 15 minutes on the clock.
And it got better for the home fans soon after when King cantered through some non-existent Leinster defence for the Scarlets’ fourth.
Leinster at this point were staring down the barrel of a record hammering, but Ireland wing Denis Hickie managed to pick off a stray Dwayne Peel long pass and race 60 metres unopposed for his side’s lone strike of a hugely entertaining first period.
Adrift 27-7 at the turnaround Leinster needed to get on the scoreboard first and they managed it with Hickie’s second after smart work around the fringe.
Scrum-half Peel suffered a serious hand injury in the process and with Wales coach Gareth Jenkins a concerned onlooker, it did not look good for the Lions star.
It needed some desperate Scarlets defence to keep Hickie out for his third soon after before Jones settled the home side with a penalty from straight in front.
But Leinster kept coming back and a quick tap by lively replacement scrum-half Chris Whitaker saw lock Trevor Hogan cross on 64 minutes.
SCARLETS: Ceiron Thomas; Mark Jones, Matthew Watkins, Regan King, Dafydd James; Stephen Jones, Dwayne Peel; Iestyn Thomas, Matthew Rees, Craig Dunlea, Inoke Afeaki, Scott Macleod, Simon Easterby (capt), Gavin Thomas, Alix Popham.
Replacements: Deacon Manu for Dunlea (40), Ken Owens for Rees (83), Adam Jones for Afeaki (40), James Bater for G. Thomas (78), Clive Stuart-Smith for Peel (46)
LEINSTER: R Kearney; L Fitzgerald, K Lewis, M Berne, D Hickie; F Contepomi (capt), G Easterby; R McCormack, H Vermaas, W Green, T Hogan, O Finegan, S Keogh, K Gleeson, J Heaslip.
Replacements: R Corrigan, B Jackman for Vermaas (40), A Byrnes for Hogan (75), N Ronan for Keogh (75), C Whitaker for Easterby (23), C Warner for Fitzgerald (83), G Brown for Kearney (11).