Australia survived a rousing second-half fightback from Argentina to register a 29-15 victory at Twickenham that sets up a World Cup final against old foes New Zealand next Saturday.
Adam Ashley-Cooper's hat-trick and a touch down by Rob Simmons helped the Wallabies reach the sport's global showpiece for the first time since 2003, but their fans were subjected to some nerve-shredding moments.
Roared on by an animated Diego Maradona who was watching from the stands, Argentina pegged back a 19-9 half-time deficit through the boot of Nicolas Sanchez and from the 54th minute they trailed by only a converted try.
But as they pressed for the precious score they needed to make their final debut, they were caught on the counter with eight minutes remaining by an inspired mazy run from Drew Mitchell with man of the match Ashley-Cooper on hand to complete his hat-trick.
The Wallabies, who were lifted by the return of David Pocock and Israel Folau from injury, lost shape early in the final quarter as the Pumas threw everything they had at their Rugby Championship rivals.
Pocock was magnificent once again, enforcing Australian rule of the breakdown, although Argentina were often their own worst enemies as they needlessly coughed up the ball time and again.
And while the Pumas ran out of ideas at times, their opponents were ruthless when offered sight of the whitewash.
Twickenham willed Argentina on and had they not made such a disastrous start in which they appeared determined to self-destruct, it could have been a different outcome.
Emotion was etched on to the Pumas' faces as they sang the national anthem and it was a lack of clear-thinking that enabled Australia to plunder a try inside the opening two minutes when Simmons picked off a telegraphed pass by Sanchez to score under the posts.
As if determined to blow their chances of a showdown with New Zealand, Argentina continued to make a series of naive mistakes, the worst of which saw Sanchez take a quick penalty just yards from his line and knock-on.
From the ensuing attacking scrum, Foley - who shortly before had performed a try-saving tackle on Marcelo Bosch - floated a perfectly judged long-range pass to Ashley-Cooper who raced over in the right corner.
Argentina trailed 14-3 after just 10 minutes and the bad news continued to pour in with a groggy Juan Imhoff being helped from the pitch with what appeared to be concussion.
Two penalties by Sanchez gave the Pumas hope, but this faded once more when lock Tomas Lavanini was sent to the sin-bin by Wayne Barnes for an illegal tackle on Folau, an act that resulted in jeers for the English referee from the pro-Argentina crowd.
Australia took the bold step of sending successive penalties into touch instead of going for goal and while the move did not immediately pay off, eventually the reward came.
After repeatedly switching the point of attack, holes began to appear in the Pumas' defence and Matt Giteau intelligently capitalised on an overlap by flinging a long pass to Ashley-Cooper for the wing's second try.
Argentina lost captain Agustin Creevy to injury, but there was an irrepressibility about their play and only desperate tackles prevented wing Santiago Cordero and centre Juan Martin Hernandez from scoring.
Foley missed a penalty, Australia's scrum collapsed in front of the posts and Sanchez slotted the three points as the deficit was narrowed to 19-12 amid a nervy start to the second half.
An exchange of penalties by Foley and Sanchez kept the scoreboard ticking over in a hard-fought third quarter that almost saw Argentina unlocked when Foley gathered a clever kick from Kurtley Beale, but the fly-half's final pass fell short of Ashley-Cooper.
Nerves were starting to afflict Australia, Foley steering a drop-goal off-target before Folau kicked into his own player to concede accidental offside that allowed the Pumas to renew their attack.
Argentina continued to be hamstrung by their error-count as they repeatedly coughed up possession and they were eventually caught on the counter with Mitchell blazing a trail into the 22 before supplying Ashley-Cooper with the final pass.
Australia had done enough to win and refused to allow their line to be breached as the Pumas pounded away in the final minutes.