They will play England or France in Auckland next Saturday.
But last-four status continues to elude Ireland, who have yet to reach the World Cup's penultimate knockout stage from seven attempts.
As they had done all through the tournament, Wales put an emphasis on attack, and their bold approach was again rewarded through tries for wing Shane Williams, scrum-half Mike Phillips and centre Jonathan Davies.
Fly-half Rhys Priestland kicked two conversions and full-back Leigh Halfpenny booted a long-range penalty to thwart an Irish side on level terms after 50 minutes when wing Keith Earls claimed a try that Ronan O'Gara converted, adding to an earlier penalty.
But Ireland, pool stage conquerors of Australia, gained little change from a colossal Welsh defence, and their revered back-row of Stephen Ferris, Sean O'Brien and Jamie Heaslip rarely featured.
Wales, in contrast, had heroes everywhere, most notably Phillips, who produced the performance of his career, and centre Jamie Roberts, whose awesome midfield power was often too much for Ireland to hold.
On this form, Wales will fancy their chances of reaching the final, an achievement that appeared fanciful in the extreme only a few months ago.
But coach Warren Gatland and their inspirational captain Sam Warburton continue to build a squad that now appears to have irresistible momentum.
Wales made a scintillating start, scorching ahead inside three minutes following a sustained passage of play that had the blockbusting Roberts as its central figure.
Twice Roberts ran aggressively at the Irish defence, the second time leaving Ireland lock Donncha O'Callaghan reeling from the effects of trying to stop him, and when possession was moved wide Halfpenny sent Williams over.
It was the Ospreys try machine's 56th touchdown for Wales - an ongoing record - and with Priestland slotting the touchline conversion, Wales led 7-0.
Ireland, though, responded by laying siege to Wales' 22, testing their opponents' defensive structure, but some thunderously-committed tackling ensured Wales stayed ahead approaching the end of a frantic opening quarter.
It proved a rip-roaring contest, with both teams maintaining impressive form that saw them qualify from tough pools, yet Ireland continue to threaten more in attack.
Centre Gordon D'Arcy roamed into space before Wales' defensive numbers closed him down, then full-back Rob Kearney galloped clear, only to be scythed down by Halfpenny's tackle.
An O'Gara penalty finally opened Ireland's account after 23 minutes, a reward for some admirable attacking endeavour that matched Wales' initial approach.
Ireland had plenty of possession, yet their dangerous backs could not break the final tackle, and Wales regained a seven-point advantage when Halfpenny landed a penalty from just inside the opposition half.
The game was played at a furious tempo, asking questions of both sides' fitness levels with more than half the contest still remaining, but Wales comfortably repelled a few late Irish flurries to lead 10-3 at the break.
Ireland blasted out of the blocks from the restart, piling into rucks at breakneck pace, and such commitment was rewarded when they drew level after 45 minutes.
Lock Paul O'Connell played a pivotal role, smashing into the heart of Wales' defence, and despite a wayward pass from scrum-half Conor Murray, Ferris and Tommy Bowe managed to work Earls clear.
The Munster wing had just enough in the tank to get there, touching down despite Phillips' attempted tackle, although referee Craig Joubert required confirmation from television match official Giulio de Santis before awarding it.
O'Gara made the touchline conversion attempt look easy, and with Ireland level at 10-10, the game was once again balanced on a knife edge.
But Wales responded magnificently, reclaiming the lead in opportunist fashion just six minutes later after brilliant work by Phillips.
The livewire number nine collected possession from a ruck, and spotting a gap in Ireland's defence he went for broke, diving over the line and touching down one-handed for a try that again needed video confirmation.
Priestland could not add the extras, yet Wales had rediscovered their early snap and verve, with Ireland now having it all to do ahead of a double substitution that saw O'Gara and Murray replaced by Jonathan Sexton and Eoin Reddan.
Priestland then missed a golden chance to increase Wales' advantage when his angled 25-metre penalty kick hit the post, handing Ireland a reprieve and ensured no let-up in the drama.
But Wales struck again 16 minutes from time after initial high-class work by Phillips, and Davies predictably showed Ireland prop Cian Healy a clean pair of heels to claim his team's third try.
Priestland converted, and at 22-10 ahead, Wales had control of the game for perhaps the first time before closing out the contest and claiming a stunning win.
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