Argentina, who topped Group C ahead of Poland, Mexico and Saudi Arabia, made it through the Round of 16 courtesy of Alvarez’s second half goal and Lionel Messi’s fine finish before the break in his 1,000th career game.
Ake awaits Alvarez after the Netherlands defeated USA 3-1 in the earlier Saturday game.
That last eight clash will take place at 19:00 next Friday in Lusail Stadium.
Messi scored the opening goal – his 789th - in the 35th minute and it was his first ever strike in a World Cup knockout game.
He fired home after being teed up by former City centre-half Nicolas Otamendi.
City forward Alvarez came off the bench in the first two games – a 2-1 loss to Saudi Arabia and a 2-0 win over Mexico – before making it into the starting line-up for the 2-0 victory over Poland in the final group match.
He kept his place for this Round of 16 encounter and justified the selection when he doubled his team's advantage on 57 minutes with a clever poacher’s finish after a mistake by keeper Mat Ryan.
The Aussies did pull one back on 77 minutes as Craig Goodwin's 25-yard shot deflected home off Enzo Fernandez.
But Argentina held on - with chances for both sides before the final whistle blew.
Alvarez, who played 71 minutes, has now helped Argentina go at least one stage further than they reached in the last tournament in 2018, where they were beaten by eventual winners, France at this point.
It was always going to be a tough ask for opponents, Australia, especially when you consider their record against Argentina.
Their only win in seven games against the South Americans was in their first meeting in 1988 – and current Socceroos boss Graham Arnold played in that match.
Alvarez and Argentina now look ahead to Friday’s last eight clash as they aim to win their third World Cup.
Their two previous victories came in 1978 as hosts and in 1986, when Maradona shone in Mexico. They’re been runners-up three times, too, in 1930, 1990 and 2014.