Argentina had gone into the semifinal with some confidence -- soccer legend Maradona flying in to watch the match -- but never truly recovered from a shocking start.
Before the game was even 10 minutes old, Australia had capitalized on two costly Argentina errors to build a lead that proved to be insurmountable.
A poorly placed pass inside two minutes allowed Bill Simmons to intercept and score the opening try after just 67 seconds -- the fastest try at Rugby World Cup 2015.
Australia pounced on another Argentina error eight minutes later, this time scrum-half Martin Landajo knocking on after attempting a tap and go.
From Australia's scrum, Bernard Foley's looping pass to Ashley-Cooper -- the eventual man of the match -- allowed the wing to go over and extend the lead.
Maradona appeared on the big screen just before the quarter hour mark and whipped the Argentina fans into a frenzy, beating his chest and leading the chants to "ole ole ole, Pumas Pumas."
However, Argentina continued to appear nervous, Australia turning over far too easily on several occasions. Unforgivable mistakes that, in a World Cup semifinal, won't go unpunished.
There was misfortune too. Quarterfinal star Juan Imhoff was forced off on 18 minutes after a knee to the head made him too groggy to carry on.
Referee Wayne Barnes then awarded Tomas Lavanini a contentious yellow card on 26 minutes, a decision that drew huge boos from around an increasingly audible pro-Argentina Twickenham.
And on the half hour, captain Agustin Creevy was to be forced off with injury and Australia made them pay.
Matt Giteau found Ashley-Cooper on the wing with a pinpoint pass for his second try of the game, but at the half three penalties from the impeccable boot of fly-half Nicolas Sanchez had left Argentina trailing just 19-9.
Los Pumas had also wasted an excellent chance of a try to give them even greater heart for the second half.
Santiago Cordero broke through the Australian ranks and offloaded to Juan Martin Hernandez.
'El Mago's' flash pass was wide of Joaquin Tuculet's hands and he fumbled the ball behind him. A simple pass would have surely allowed Tuculet to stroll through and score.
Australia's indiscipline -- which may cost them dear in the final against New Zealand -- continued at the start of the second half, as a collapsed scrum allowed Sanchez to again gnaw away at the lead.
It continued to be a case of missed chances for Argentina, so often getting close to the posts but unable to capitalize, relying on Sanchez, who eventually kicked five penalties, for points.
Australia, on the other hand, had been clinical all game and were again after 72 minutes.
A tremendous break away by Drew Mitchell tore the Argentina defense to shreds and set Ashley-Cooper free on the wing to complete his hat trick -- and score his 11th career World Cup try.
The deafening Argentina support didn't let up for an instant, despite the game now out of their reach and the players on the pitch didn't let up either.
They continued to attack but failed to turn good moves and positions into tries.
Maradona was eventually seen shedding tears, as was Argentina coach Daniel Hourcade and several members of his team, including talisman Sanchez.
However, the Pumas, who earned their nickname after a British journalist mistook a jaguar for a puma, have proved they are the real deal and a major force in world rugby.
"I feel very proud of what the team has achieved but Australia played really well," said Hourcade.
"I think we are on the right path. We're on a learning curve. Our legacy [to this tournament] is the way we played the game."
The third-fourth playoff against South Africa awaits for his team Friday, while the Wallabies will bid to end their Anzac rivals hopes of winning a second World Cup in a row.
Coach Michael Cheika, credited with reviving the Australians, knows that it will be a formidable test.
"New Zealand are well drilled. They have an excellent coach and know what they're doing all over the on pitch. We need to improve," he said.
"We believe in ourselves to go out there and do our absolute best. I don't want to look back at our last win against the All Blacks because I'll have to look at the other nine defeats. We're looking ahead to Saturday."