Expansive and scintillating play backed up by the boot of Nicolas Sanchez, who kicked four conversions and five penalties, gave the Pumas a deserved 43-20 win at the Millennium Stadium in Cardiff.
It's the second time in its history Argentina has reached this stage. Daniel Hourcade's team will now meet Australia next weekend, after the Wallabies edged past luckless Scotland 35-34 in a pulsating match at Twickenham later Sunday.
For a nation better known for its football exploits, it is a remarkable achievement for Argentina, celebrated by its most famous exponent of the round ball game, Diego Maradona, who has promised to fly back for the semifinals after earlier seeing them thrash Tonga in a pool match.
Maradona would have been hard put to have matched the flair and enterprise the Pumas showed to build up a quick 17-0 lead over the stunned Irish.
Matias Moroni and Juan Imhoff ran in two tries, both converted by impeccable flyhalf Sanchez, who also landed a penalty.
Ian Madigan, in for the injured and badly missed Johnny Sexton, kicked the first points for the Irish, but another Sanchez penalty took Argentina 20-3 clear.
Either side of half time, the injury-depleted Irish enjoyed their best spell of the quarterfinal, as Luke Fitzgerald and Jordi Murphy went over for tries.
With Madigan making the conversions, the Pumas only led by three points, but in a similar pattern to the start of the match, Joaquin Tuculet and Imhoff crossed in the closing moments and man of the match Sanchez made no mistake with the extra points, plus a late penalty.
It left a winning margin of 23 points, but Imhoff admitted it had been a closer encounter than the score suggested.
"It was a very tough game and worked hard to get this victory," he told UK match broadcaster ITV Sport. "We will enjoy this moment but we will have another very difficult match next weekend."
Ireland captain Jamie Heaslip -- standing in for injured and much missed Paul O'Connell -- said his team had paid for the start and finish of the match.
"Argentina play a very expansive game and stretched us and we didn't make it easy for ourselves at times.
"But fair play when we got back to three points they took their opportunities to kick on and we couldn't take ours," he said.
Australia was a heavy favorite to beat underdog Scotland, but needed a 79th minute penalty from Bernard Foley to seal victory and underline the dominance of Southern Hemisphere rugby in rugby's four-yearly global showpiece.
Host England did not even make it out of the pool stages, while Wales came up short in a hard-fought quarterfinal with South Africa Saturday.
Scotland, however, went out of the tournament with heads held high after a never-say-die performance, leading 34-32 with seven minutes remaining after Mark Bennett's try from an interception, converted by Greig Laidlaw in his 19-point tally.
A controversial decision by referee Craig Joubert to award Australia a penalty for offside presented Foley with the chance to win the match and he duly slotted the kick, under immense pressure, through the posts.
It spelled bitter heartbreak for Scotland, who led 16-15 at the half and always stayed in the match when Australia turned up the heat after the interval, running in two more tries to take its tally to five, with Foley finally getting his range with the boot, including the vital late kick.