The Socceroos lost their Group D opener to world champions France, but they then beat Tunisia and Denmark 1-0 to finish on six points, which was enough to claim second spot in the section.
Australia previously advanced to the round of 16 in 2006, but they have never made the final eight, so the national side will be looking to create history against Argentina this weekend.
Here, Sports Mole looks at some reasons for Graham Arnold's side to be confident of reaching the quarter-finals of the competition.
Recent form
Australia found it difficult in their competition opener to France, but their response to the setback was incredibly impressive, with Mitchell Duke's clever header handing them a 1-0 success against Tunisia, before Arnold's team beat Denmark courtesy of a strike from Mathew Leckie.
Denmark were fancied by many to be potential dark horses at the competition, but it was a brilliant display from the Socceroos, who held firm at the back to keep a clean sheet.
Australia have now been victorious in seven of their last eight matches in all competitions, which includes the wins over United Arab Emirates and Peru during qualification for the World Cup.
The Socceroos have become used to winning in recent matches, which is certainly a good habit, and the fact that they will enter this game off the back of successive victories should fill them with confidence.
There is also no pressure on Australia, it is very much a free hit, and Saudi Arabia showed earlier in the competition that this Argentina side are beatable despite their immense pedigree.
Lionel Messi's failure to score in knockout round of World Cup
Lionel Messi has been in strong form for Paris Saint-Germain this season, scoring 12 goals and registering 14 assists in 19 appearances in all competitions.
Meanwhile, the 35-year-old has already netted twice and provided one assist in three appearances at the World Cup, finding the back of the net against Saudi Arabia and Mexico.
Messi missed a penalty against Poland last time out, though, and he has actually never scored in the knockout round of a World Cup, with his eight goals in the tournament coming in the group stage.
The attacker has now had 23 efforts without finding the back of the net in the knockout round, which he will be desperate to put right on Saturday.
However, if Australia can keep Messi quiet, then the Socceroos will certainly have a much better chance of progressing to the quarter-finals of the tournament.
Strong form of Harry Souttar, Mathew Leckie
Australia have had many standout performers during the tournament. Indeed, they would not be present at this stage had a number of players not been in excellent form.
Harry Souttar has been terrific at the back, though, with the 24-year-old's form even more impressive considering that he only returned from a serious knee injury for Stoke City last month.
Australia, as mentioned, have kept back-to-back clean sheets, while they have produced shutouts in five of their last six matches.
The Socceroos also have talent down the other end of the field, with Leckie hitting the winner against Denmark, and the attacker is now only one of just three players to score and assist for Australia in a single World Cup, joining the company of Tim Cahill and John Aloisi.
The 31-year-old's finish against Denmark will be remembered as one of the great World Cup moments for Australia, and he will be bidding to score a second World Cup goal on Saturday.
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