Australia led 19-9 at half-time after Rob Simmons’ early try was followed by two from Ashley-Cooper.

Ashley-Cooper's third try, 10 minutes from time after a brilliant run by Drew Mitchell, sealed the win for the reigning southern hemisphere Rugby Championship title holders.

In one of the tries of the tournament, Mitchell received the ball in his own half and set off on a scintillating diagonal run. He wrong-footed four Pumas players and with only one defender left to beat unloaded to Ashley-Cooper to ensure the try that would put the game out of Argentina’s reach.

Fly-half Nicolas Sanchez kicked all of the Pumas’ points from five penalties in front of an 80,025 crowd that included Argentina football great Diego Maradona.

A dry day made for ideal running rugby and it took Australia just 68 seconds to score the game’s first try when lock forward Simmons intercepted Sanchez’s inside pass. Bernard Foley added the easy conversion and Australia led 7-0.

Fly-half Foley was then involved at the other end when, after Argentina exploited a huge gap in Australia’s cover, he made a try-saving tackle on Marcelo Bosch. But an offence in the build-up led to a penalty for Sanchez.

The Wallabies boosted their lead in the ninth minute, winning a scrum, and Foley’s long pass freed Ashley-Cooper for a try in the corner.

Foley kicked a tricky conversion and Argentina found themselves on the receiving end with Australia in charge at 14-3.

The Pumas suffered another setback when in-form wing Juan Imhoff went off injured in the 18th minute.

Argentina forced a 23rd-minute scrum penalty and Sanchez, becoming the tournament’s leading points scorer as he passed the 79-point tally of Scotland’s Greig Laidlaw and South Africa’s Handre Pollard, cut Australia’s lead to 14-6.

Argentina, however, found themselves a man down in the 26th minute when lock Tomas Lavanini was sent to the sin-bin by referee Wayne Barnes for a “no-arms” tackle on Folau.

Things got worse for Argentina when influential skipper and hooker Agustin Creevy went off on the half hour mark.

Australia took over Argentina’s 22 and the pressure told when Matt Giteau sent another miss-pass for Ashley-Cooper to get his second try.

Sanchez got a third penalty and at the break Australia led 19-9, a deficit no team has overcome to win in the World Cup.

In the second half, Sanchez kicked two penalties either side of a Foley effort to leave Australia 22-15 in front.

Argentina pressed hard in the final quarter but Mitchell’s brilliant run to set up Ashley-Cooper’s hat-trick put the result beyond doubt.

Australia will be immediately plotting a game plan against New Zealand. As well as their first meeting in a World Cup final, both countries will be seeking to become the first to win the tournament three times.

“Tonight we can think we have given ourselves the opportunity to play in a World Cup final and we will work out how we are going to do it against a pretty dynamic team,” said Cheika of the next challenge.

He praised the Australian defence. “They tore Ireland apart last week and we had to work hard to stop them working a try.”

But he also said too many penalties were given away. “Penalties are a part of the game and we gave away too many in the first half. We tried to rectify that in the second half. We did a little bit, but we still gave away a few too many.”

Argentina, a revelation at the World Cup who beat Ireland 43-20 in the quarter-finals, now play South Africa in the third place playoff on Friday. Their showing has proved the worth of their move into the Rugby Championship against Australia, South Africa and New Zealand.

“I am absolutely satisfied, absolutely proud of what this team did,” Pumas coach Hourcade said. “We stayed faithful to our style of play. They deserve a lot of praise. Australia are a great team.”