In an exciting and tense climax to the play-offs, first half tries from Tommy Bowe and man-of-the-match Lee Byrne did the damage as the Ospreys deservedly ended the season with silverware.
It was a frustrating way for Michael Cheika to end his coaching tenure at Leinster, and in an error-strewn display the home side could only must four penalty goals from Jonathan Sexton.
Sexton's opposite number Dan Biggar converted the two tries for a 14-3 half-time lead and landed a second half penalty as the Welsh region completed a clean sweep of away victories over Irish sides this season.
The Ospreys came to Dublin hoping to end a six-match losing run against Leinster, and head coach Sean Holley put his faith in the team that suffocated Glasgow Warriors into submission in the semi-final.
Leinster made one enforced change to the side that accounted for Munster last time out, with Springbok prop CJ van der Linde replacing stomach bug victim Cian Healy.
The Ospreys, with director of rugby Scott Johnson a welcome sight on the sideline, enjoyed an early bout of pressure in the hosts' 22. Bowe popped up in the middle in a move which led to Biggar darting in under the posts - but play was called back for a knock on from Marty Holah.
Leinster showed their solidity in the scrum and lineout and a clever attack released Shane Horgan for a one-on-one with Shane Williams, only for Isa Nacewa to be whistled up for a forward pass in the build-up.
Both sides were guilty of some poor kicking in a breathless opening quarter, and the pace was ramped up further as Rob Kearney countered brilliantly and Williams then threatened as he chased his own kick.
Biggar had the first scoring opportunity but fluffed his lines as he pushed a left-sided penalty narrowly wide from just outside the 22.
There was a huge cheer as the retiring Malcolm O'Kelly crunched Mike Phillips after a quickly-taken lineout, but Leinster were being regularly penalised at the breakdown and the Ospreys soon broke the deadlock.
Back within sight of the Leinster 22, a flat delivery from Biggar sent Andrew Bishop bursting past Gordon D'Arcy and faced by Kearney, the centre's well-timed pass to the left put Bowe charging over for a 19th minute opener.
Biggar converted but Sexton quickly replied by firing over from the ten-metre line, following a high tackle by Byrne on his opposite number Kearney.
But the Ospreys continued to look the more dangerous with ball in hand and they missed out on a glorious chance to nab try number two when Alun Wyn Jones and Jerry Collins failed to use numbers out wide.
There was no such indecision, six minutes before the break, as the Ospreys clinically countered from halfway to tee up Byrne for a sumptuous score.
Biggar floated a long pass out to the right where James Hook took it on before popping it back inside for his full-back to thunder away from D'Arcy's grasp and evade a last-gasp tackle from Jamie Heaslip on the way to the try-line.
Biggar's successful conversion pushed the visitors into a well-earned 14-3 lead, with Bishop, Holah and Byrne leading the charge.
Leinster lost both Kevin McLaughlin (knee) and his replacement Stephen Keogh (ankle) to injury, but made a positive start to the second half as Sexton popped over a long range penalty.
A Leinster offside allowed Biggar restore his side's advantage to 11 points and handling errors blighted the home side's play as they became increasingly desperate in a flooded midfield.
The Ospreys were content to soak up the pressure, with Hook and Byrne miscuing drop goal attempts, and Leinster finally got into a rhythm on the hour mark. D'Arcy went on a 30-metre burst and the forwards edged closer, before Sexton landed his third penalty.
Byrne was fortunate to avoid a yellow card as he caught D'Arcy around the neck as the Leinster centre broke the line once again. Sexton converted the resulting penalty, with nine minutes to go, and the momentum was clearly with Cheika's side.
However, the Ospreys used their experience to keep them at arm's length and Sexton's failure to convert a fifth penalty in the dying minutes summed up the hosts' night.
With forwards coach Filo Tiatia getting on for his 99th and final appearance, the Welshmen held on to claim their first win in Dublin in five years, founded on a clever game-plan, attacking guile and plenty of forward grunt.
|Leinster Rugby Score Card|
|Ospreys Score Card|