Fly-half Jonathan Sexton's 70th-minute penalty proved to be the difference between two evenly-matched sides as Leinster ran out 19-16 winners in front of a crowd of 66,523 at Murrayfield Stadium.
Both sides scored a try each through Ben Woods and Jamie Heaslip, with Julien Dupuy and Sexton adding 11 points each with the boot after Brian O'Driscoll had opened the scoring with a third-minute drop goal.
Leicester led 13-9 at the half-time interval courtesy of a late converted try from Woods. The former Newcastle Falcons openside powered over from 15 metres following a period of sustained pressure from the Tigers.
Centres Dan Hipkiss and Ayoola Erinle paved the way for the opening try of the match with a powerful burst apiece while the Leicester forwards retained possession for a number of phases despite impressive initial resistance from Michael Cheika's men.
Tigers fly-half Sam Vesty's offload was read perfectly by Woods who ran straight through Isa Nacewa's tackle before planting the ball down five metres to the right of the uprights.
Dupuy added the simple conversion to move Leicester four points clear with just over a minute of the half remaining.
Leinster had enjoyed the brighter start to the match and opened up a 9-3 lead through two contrasting drop goals and a Sexton penalty.
Ireland skipper O'Driscoll was the first man to put points on the board, firing a 25-metre drop straight through the posts with six minutes played.
Having sent an earlier penalty attempt narrowly wide of the posts, Dupuy levelled the scores with a second effort three minutes later after Luke Fitzgerald had spilt a Geordan Murphy up and under and Hipkiss had followed up with another powerful burst.
Sexton restored Leinster's advantage after 17 minutes through a superbly-struck drop goal from right on halfway. The 23-year-old outside-half played a starring role in the semi-final win over Munster following an early injury to Felipe Contepomi and he certainly appeared to have retained his confidence as he made Vesty pay for a failing to find touch.
Leinster's three-point lead became six with 24 minutes on the clock as Sexton knocked over a simple penalty after Leicester had made no effort to roll away when Leinster quickly transferred play from right to the left following a typically-robust charge from Heineken man-of-the-match Rocky Elsom.
A Stan Wright sin-binning then turned the tide in Leicester's favour eight minutes before the break when the Cook Islands prop tackled Vesty off the ball inside the Leinster 22. The Tigers had looked to be under serious pressure just moments earlier but a piece of individual brilliance from Hipkiss turned defence into attack in an instant.
The England international stepped inside Leinster's drift defence just 10 metres from his own line, sprinted into opposition territory and then threaded a telling kick towards the try line. Sexton had little option but to hack the ball into touch, giving Leicester a five-metre lineout from which Wright would receive his yellow card two phases later.
After registering seven points in the first half while Wright was marooned on the sidelines, Leicester added a further three within minutes of the start of the second period. A straightforward penalty from Dupy made it 16-9 to Leicester with 43 minutes gone before Leinster hit back in impressive style five minutes later.
A patient build up from the Leinster forwards culminated in Heaslip crashing over in an almost identical position to where Woods had scored in the first half. The British & Irish Lions No8 sent the Leinster section of the crowd wild before Sexton converted to bring they sides level once more with just over half an hour remaining.
Both defences stood resolute for the next 20 minutes before Sexton secured a place in Leinster folklore with 10 minutes left to play. The young playmaker kept his composure to move Leinster three points clear from and eventually ensure it was they, and not the 2001 and 2002 Heineken Cup winners, who would be crowned Kings of Europe in 2009.