A masterful performance from Ruan Pienaar guided Ulster past Edinburgh 22-19 and into their first Heineken Cup final since they were crowned European champions in 1999.
The South African scrum-half kicked 17 points and pulled the strings behind a dominant pack as Ulster booked a place at Twickenham on 19 May.
Ulster, who brought a huge crowd with them to Dublin, will face either defending champions Leinster or Clermont Auvergne in the final.
Edinburgh produced a spirited performance, with four penalties from fly-half Greig Laidlaw keeping them in touch after Pedrie Wannenburg's try had put Ulster ahead.
But the Scottish side, making their first appearance in the semi-finals, failed to take their chances and Ulster - inspired by man of the match Pienaar - turned the screw after the interval.
Ulster's victory was ultimately more comprehensive than the final score suggested, after Edinburgh replacement Jim Thompson crossed for a consolation try in the final minute.
But it did nothing to dampen the Ulster celebrations.
Ulster flexed their scrummaging muscles from the outset, earning Pienaar his first shot at goal after five minutes and the South African landed the kick from halfway with plenty to spare.
Laidlaw responded with two successful kicks to put Edinburgh briefly ahead, the second earned by Grant Gilchrist at the ruck after a tackle from Netani Talei had stopped an Ulster attack dead.
With the wind gusting into the Aviva Stadium, both sides kicked a lot of ball but when Ulster secured a strong attacking platform, with a scrum on the Edinburgh 22, their pack went to work.
Pienaar attacked left to stretch the Edinburgh defence, wing Craig Gilroy then charged onto an inside ball and when Wannenburg was wrapped up by Edinburgh he earned another scrum.
The South African number eight just about kept control of the ball at the base as Ulster drove forward before picking up to barge his way over the line.
Pienaar converted and then charged down a box-kick from Mike Blair to keep Ulster on the front foot but they wasted a two-man overlap.
Edinburgh's success in the Heineken Cup had come from being positive and they responded to that let off by working through 18 phases to build the pressure on Ulster.
From a five-metre scrum, Laidlaw released Lee Jones before Gilchrist charged for the line but lost possession and Pienaar cleared 50 metres into touch.
Terblanche was dispatched to the sin-bin after the officials spotted his striking Ross Ford at a ruck and although Edinburgh kept hammering away they could not make the extra man count.
Tim Visser was a constant threat, racing into the Ulster 22 before Talei charged forward but he dropped it three yards short of the line.
Ulster not only survived their sin-bining unscathed but Pienaar landed his second penalty just before Terblanche returned after Jones had been caught marginally off-side.
Stephen Ferris was fortunate not to follow Terblanche into the bin after conceding a cynical penalty following Ross Rennie's charge into the 22.
Laidlaw ended the first half with a successful penalty and started the second in similar fashion to bring Edinburgh within three points.
Andrew Trimble could not quite hold onto Paddy Wallace's pass to finish off a slick Ulster attack and the dominant Irish scrum was then penalised.
But Pienaar thrust them back on the front foot, chasing his kick downfield and tackling Tom Brown into touch to earn Ulster the attacking lineout.
But Edinburgh defended ferociously, twice stopping Dan Tuohy short of the line before Laidlaw brilliantly ripped the ball off Wannenburg underneath his own crossbar.
The power of the Ulster scrummage earned them another penalty which Pienaar landed, before a brilliant box-kick to the corner pushed Edinburgh onto the defensive again.
And when referee Romain Poite penalised Edinburgh for bringing down Ulster's driving lineout, Pienaar stepped up again to open a decisive seven-point lead just past the hour mark.
Fittingly, the Ulster pack hammered the nail into Edinburgh's coffin, winning another scrum penalty for Pienaar to land from 35 metres.
Talei's charge led to Thompson's late consolation but it was too little too late.