David Kearney's second-half try ensured that Leinster will have the chance to become the first team to do the European and domestic double since Wasps in 2004 as they beat Glasgow 19-15 at the RDS.
Joe Schmidt's side will return to Dublin for the Pro12 final against the Ospreys in a fortnight's time after their Heineken Cup final against Ulster next Saturday.
Jonathan Sexton kept the scoreboard ticking over against the Warriors, finishing with 14 points, before Kearney got the key score 15 minutes from time.
Glasgow managed only a single penalty from Duncan Weir before Dougie Hall and Stuart Hogg grabbed late consolation tries with game already gone.
The Warriors had beaten Leinster 23-19 at the RDS back in September and were clearly not overawed by the occasion in their second semi-final in three years.
However Leinster soon settled into their rhythm and put Sean Lineen's side under huge pressure in the first half.
Glasgow do not have the best defence in the Pro12 for nothing and showed incredible resolve to keep the reigning European champions at bay for large periods.
Even when young centre Alex Dunbar was sent to the sin bin after a series of penalties conceded by the Scots, Glasgow refused to buckle and Leinster could only manage three points.
It was the home side who had taken an early lead through Sexton, the Irish international on target with his first penalty attempt after just seven minutes.
Glasgow were back on level terms two minutes later as Leinster conceded a penalty from the restart and Weir made no mistake.
Joe Schmidt was then dealt a blow as Gordon D'Arcy limped off to be replaced by rising star Ian Madigan midway through the half before Sexton put Leinster back in front.
Dunbar was then temporarily sent from the field as he prevented a quick release when Glasgow were under pressure but Leinster could manage just three more points before the break.
And despite dominating possession and territory early in the second half they struggled convert their chances into points.
On a rare incursion into Leinster territory Weir missed a long-range penalty, and was again off-target from closer in two minutes later.
However he was not the only man to lose his radar, with Sexton hooking a gettable penalty just before the hour.
Schmidt also had to contend with two more injuries, Cian Healy and Eoin O'Malley both being forced off, a concern ahead of two finals in as many weeks.
Sexton was back on target on 62 minutes when Alastair Kellock went a fraction too early to put pressure on Eoin Reddan at a ruck, Leinster led 12-3.
And with a quarter of an hour to go Leinster took their chance when Isa Nacewa spotted a match-up with Kellock in the backline and sent Kearney over in the corner. Sexton added the conversion from the touchline to put Leinster three scores clear.
They almost added a second two minutes later as Andrew Conway collected a cross kick and dotted down but was ruled to have been offside as the ball was kicked.
Glasgow showed some fight to get a try three minutes from time as replacement hooker Hall dived over in the corner before Hogg was quickest on to Ruaridh's Jackson's grubber for a try with the last play of the game.
However it was not enough and Leinster will take on the Ospreys for the Pro12 title in a fortnight in Dublin.
Pens: Sexton 4
For Glasgow Warriors:
Tries: Hall, Hogg
Leinster: 15 Isa Nacewa, 14 Fergus McFadden, 13 Eoin O'Malley, 12 Gordon D'Arcy, 11 David Kearney, 10 Jonathan Sexton, 9 Eoin Reddan, 8 Jamie Heaslip (captain), 7 Shane Jennings, 6 Sean O'Brien, 5 Devin Toner, 4 Brad Thorn, 3 Mike Ross, 2 Richardt Strauss, 1 Cian Healy.
Replacements: 16 Sean Cronin, 17 Heinke van der Merwe, 18 Nathan White, 19 Leo Cullen, 20 Kevin McLaughlin, 21 Isaac Boss, 22 Ian Madigan, 23 Andrew Conway.
Glasgow: 15 Stuart Hogg, 14 Federico Aramburu, 13 Alex Dunbar, 12 Graeme Morrison, 11 DTH van der Merwe, 10 Duncan Weir, 9 Chris Cusiter, 8 John Barclay, 7 Chris Fusaro, 6 Rob Harley, 5 Al Kellock (captain), 4 Richie Gray, 3 Mike Cusack, 2 Pat MacArthur, 1 Ryan Grant.
Replacements: 16 Dougie Hall, 17 Jon Welsh, 18 Moray Low, 19 Tom Ryder, 20 Henry Pyrgos, 21 Johnnie Beattie, 22 Ruaridh Jackson, 23 Peter Murchie.
Referee: George Clancy (Ireland)
Assistant referees: John Lacey, Leo Colgan (both Ireland)
TMO: Marshall Kilgore (Ireland)
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