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But they were forced to hang on amid a nerve-shredding climax as Wales fly-half Stephen Jones missed a 50-metre penalty with the game's final kick.
Fly-half Ronan O'Gara's drop-goal won the game for Ireland after Wales led 15-14, but it was captain marvel Brian O'Driscoll who fittingly set the ball rolling.
O'Driscoll touched down for Ireland's second-half opener, before wing Tommy Bowe added a second try just two minutes later.
O'Gara slotted both conversions, sinking defending champions Wales, who remained in the contest through four Jones penalties before his late drop-goal.
Wales led 15-14 entering the closing stages, but O'Gara came up trumps when it really mattered as Ireland emulated the achievement of Karl Mullen's Ireland team in 1948.
Ireland's victory also consigned Wales to a lowly fourth place championship finish just a year after winning the Grand Slam.
England finished second, with France third courtesy of Les Bleus' emphatic victory over Italy in Rome earlier today.
Wales suffered a late injury blow when number eight Andy Powell was ruled out of the contest through a thigh muscle injury suffered in training yesterday.
Scarlets forward Dafydd Jones replaced him, with Ospreys flanker Jonathan Thomas moving onto the bench, but Ireland had no last-minute problems.
Confirmation of the stakes came immediately when Wales skipper Ryan Jones and Ireland lock Donncha O'Callaghan squared up following an apparent trip by Jones on O'Gara.
Ireland were awarded the penalty but O'Gara drifted his kick wide.
Ireland continued to enjoy territorial supremacy but could not make their advantage count as the opening quarter ended scoreless.
Wales threatened fleetingly and full-back Lee Byrne looked to launch his fellow backs but Ireland appeared comfortable in defence.
There were signs though, of O'Gara beginning to crumble under pressure, and Wales grew in confidence as a tense first-half drew to its close.
Jones' second penalty doubled the Welsh advantage and an enthralling opening period ended with Wales 6-0 ahead.
The home side were in the ascendancy, knowing a converted try would give them a 13-point advantage they required to deny Ireland title glory.
Ireland though, had other ideas and they wiped out Wales' advantage within three minutes of the restart.
Sustained pressure had Wales stretched defensively after a break by Bowe and O'Driscoll stretched out to claim the touchdown under pressure from Wales hooker Matthew Rees.
Television official Romain Poite confirmed the touchdown and Ireland were up and running, with O'Gara's conversion giving the visitors momentum.
And before Wales could recover Ireland struck again, leaving Wales in a state of disarray.
O'Gara had the vision to test Wales' back-three defence with a delicate kick and fatal hesitancy between centre Gavin Henson and wing Shane Williams resulted in a second Irish touchdown.
Bowe was the recipient, grasping his chance - and a kind bounce - majestically to sweep clear and take Ireland within sight of Grand Slam glory.
Wales were rocked by such a double setback but Jones soon completed his penalty hat-trick to keep the game alive, and then slotted a fourth penalty that cut the home side's deficit to just two points.
Ireland knew it was a case of trying to close the game out, but after surviving a long-range Gavin Henson penalty attempt, they could not survive any longer.
Jones' drop-goal looked to have destroyed Ireland's Grand Slam dream following a blistering break by scrum-half Mike Phillips, when he smashed through three Irish defenders.
But Ireland were not to be denied as the day culminated in lock Paul O'Connell lifting the Triple Crown trophy before O'Driscoll - fittingly - looked after the main business.
|Wales Score Card|
|Ireland Score Card|
|Brian O'Driscoll (capt)||1||5|