The west Wales outfit surged into a 14-6 lead at the interval thanks to tries from international duo Scott Williams and Liam Williams.
George North and Andy Fenby grabbed further tries following the interval as the Scarlets continued to run riot.
Devin Toner hit-back for Leinster before Kieran Murphy, North and Fenby completed the rout. Ian Madigan crossed for the
Irish province in injury time but it was a mere consolation.
The victory gave Simon Easterby his first competitive victory in charge of the Scarlets and he was delighted with the performance.
But he was also challenge the Scarlets to back their victory up against Glasgow next week.
“If we were offered that score-line, seven tries and a couple for them before the game we would definitely have taken it,” said Easterby.
“We’ve struggled in recent years against Leinster and Munster but we showed that we can mix it with them.
“But we have to be realistic as well and it’s all about building on this performance.”
Leinster got off to an assertive start at Parc y Scarlets and took the lead on three minutes, thanks to a Madigan penalty.
But the Scarlets quickly established a stranglehold on the game. They could have levelled the scores on 11 minutes but backed their set-piece and kicked to the corner.
Leinster managed to hold the surging Scarlets short but from the ensuing scrum they continued to lay siege to the try-line and centre Williams sniped through.
Minutes later he turned to provider and sent his namesake Liam over with a pinpoint pass.
Madigan landed a late penalty to bring the scores to 14-6 at the interval but the floodgates opened in the second.
North grabbed his first within three minutes of the restart and the hosts followed it up with another scintillating long-range attack, which culminated with a Fenby try.
Leinster hit-back through Devin Toner, as the Scarlets paid the price for a heavy penalty count.
But Leinster’s glimmer of hope was ended when the Welsh region put the final nail in their coffin.
A Fenby hitch-kick created an opening and he slipped a deft offload for replacement Murphy to score a minute after he came on.
North and Fenby competed the rout with two further touchdowns, which continued to demonstrate the hosts’ superiority.
Leinster continued to fight and Madigan was rewarded for his tenacity with a try at the death but it was merely a consolation.
