Graham Arnold's side defied the odds to book their spot in the last 16 in Qatar with a 1-0 win over Denmark on Wednesday that wrapped up the runners-up spot in Group D and sent them through to the next round for the first time since 2006.
Yet this was not a victory built on the attacking talents at Arnold's disposal.
While it was certainly not a smash and grab, it was a day for Australia's dogged rearguard to stand tall, which they did from the first whistle, with Souttar, born in Aberdeen to an Australian mother and Scottish father, a none-shall-pass general at the back.
Souttar is a hulk of a centre back whose performances at the World Cup have been a throwback to the days when defenders had nicknames like Psycho, Chopper and Razor, and he was once again immovable as Australia soaked up everything Denmark could chuck at them.
At 6-feet-6 inches tall (1.98 metres), Souttar, who plays in England's second tier with Stoke City, was a physically imposing presence and threw himself into tackles and blocks with a relish that modern centre backs sometimes lack.
When the ball went into the box as Denmark tried to work their way back into the match after Mathew Leckie's excellent goal in the 60th minute, it was invariably Souttar's head that connected with it.
In the 87th minute, he slid along the turf to pull off a superb tackle on Kasper Dolberg while four times in stoppage time the ball was thrown into the Australia penalty area only for Souttar to put his head in the way of danger.
The 24-year-old's all-action heroics at the World Cup, where he had already gone viral for a perfectly-timed crunch on Tunisia's Yassine Khenissi, are more remarkable given he spent nearly a year on the sidelines after suffering a cruciate knee ligament injury playing for Australia last November.
His manager has little doubt he is destined for the top.
"When you look at Harry, he's been out for a year with an ACL and he's played three games before he came in," said Arnold.
"But I just had so much belief in that boy, I know his mentality's so strong. Tell you what, if I was a Premier League club I'd be banging on the door real quick, he's that good."
His display was perhaps typical of this Australia side, and their fans, a noisy presence at Al Janoub Stadium, would be forgiven for seeing few similarities between this team and their last to make the second round 16 years ago.
That side was spearheaded by the likes of Harry Kewell, Mark Viduka and Tim Cahill, a unique set of talents who had graced the game at the highest level in England.
The current crop is more workmanlike, and as such their achievement is perhaps all the more impressive.
There are few, if any, standout stars in this side. Goalscorer Leckie, who plays his football at Melbourne City, typifies a team where the collective is more than the sum of its parts.
Striker Mitchell Duke, who scored their winner against Tunisia plies his trade in the second division in Japan while Craig Goodwin, who was on target in their defeat to France, plays for Adelaide United at home.
Yet while they may lack star quality, they have demonstrated that sometimes there is little substitute for old-fashioned organisation and a bit of hard yakka.
