Leo Cullen’s men ran in five tries and Jonathan Sexton kicked 13 points as they became the first Celtic side to win the domestic and European Cup titles in the same season.
Leigh Halfpenny booted Scarlets into an early 6-3 lead and Johnny McNicholl’s well-taken try cancelled out a Devin Toner effort, but James Lowe’s deftly-finished score on the stroke of half-time had Leinster 21-11 to the good.
Man-of-the-match Sexton stepped up as captain after injury unfortunately ended Isa Nacewa’s 185th and final Leinster appearance in the 18th minute, while Scarlets also lost Aaron Shingler to a knee injury.
The Conference B table toppers put the game beyond Scarlets’ reach with third quarter tries by Sean Cronin and Jordan Larmour, coupled with a further score by Jack Conan.
Time ran out on the defending champions’ late comeback, although the classy McNicholl finished with a hat-trick and replacement prop Werner Kruger also crossed late on.
Wayne Pivac’s charges were much improved compared to their most recent visit to Dublin – last month’s 28-13 Champions Cup semi-final defeat by the same opposition – and an early poach by James Davies offered encouragement. Yet, Sexton gave Leinster a sixth-minute lead from the tee, before Halfpenny, who shrugged off a hamstring injury to start, responded with two penalties by the 12-minute mark – rewarding flanker Shingler’s restart work and punishing a James Ryan offside.
Rob Kearney raised the decibel level among the 46,092 crowd by beating Halfpenny to a Sexton garryowen, the latter turning forward pressure into three points, but Nacewa was taken off soon after.
His replacement, Rory O’Loughlin, broke through a gap in the lead-up to Sexton’s third successful kick, which crept over via the right-hand post.
Leinster finally made their 80 per cent share of possession count on the half-hour mark, No.8 Conan launching a prolonged attack from deep. Lowe and Tadhg Furlong also had key involvements before lock Toner was driven over for an unconverted try.
Scarlets soon found joy in the outside channels, moving the ball at pace for Steff Evans and Gareth Davies to go close and set up winger McNicholl to snipe over in the 34th minute.
Halfpenny failed to convert at 14-11 and Leinster showed their champion quality, twice kicking for the corner before soft hands from McGrath and Sexton sent Lowe diving over on the short side. Sexton’s conversion wormed its way over for a ten-point split at the interval.
Despite Scarlets defending Leinster’s first wave on the resumption, Sexton found a superb touch after Scott Williams’ high tackle on the Ireland man and hooker Cronin sprang over in the right corner from the resulting maul. Sexton bent his touchline conversion through the uprights for a 28-11 advantage, and young gun Larmour’s chasing down of his own kick and terrific pick-up served up the Irish province’s fourth try.
Scarlets worked the ball wide for McNicholl to acrobatically touch down in the 64th minute, Halfpenny’s well-struck conversion giving them some hope at 33-18 down.
However, Conan slammed the door shut four minutes later, replacement Joey Carbery’s slick footwork taking him past Hadleigh Parkes before the supporting McGrath sent Conan in under the posts.
Carbery’s conversion had Leinster counting down the minutes to their first Pro14 title success since 2014, yet Scarlets deserve immense credit for their finish.
Kruger muscled over from close range for the Welsh side, then McNicholl added an injury-time seven-pointer, created by centre Williams’ barnstorming run.