Argentina - who have never beaten one of the southern hemisphere's big three in a World Cup - were their own worst enemies in an error-strewn start that saw Rob Simmons and Ashley-Cooper cross for Australia.
But the boot of Nicolas Sanchez - who slotted five penalties in all - kept the magnificent Pumas in touch, despite Ashley-Cooper's second on the half-hour mark.
In the second half the Pumas - who lost key players like Juan Imhoff, Juan Martin Hernandez and Agustin Creevy to injury during the clash - refused to buckle until a clinical Wallabies sealed the victory late on with Ashley-Cooper's third.
Victory for Michael Cheika's side sets up a fantastic World Cup final against their trans-Tasman rivals the All Blacks - the first time these two old enemies have met in the final.
But the Pumas will have won many more admirers for their fast-paced tempo throughout at Twickenham.
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