The South Koreans teed up a rematch of the 2015 Asian Cup final, which Australia won on home soil, with the dramatic comeback victory, taking the shoot-out 4-2 after a 1-1 draw.
But, surely to the delight of Socceroos coach Graham Arnold and his charges, who already had two days' extra rest after beating Indonesia on Sunday local time, they did it the long way.
Australia will have 53.5 more hours rest than South Korea heading into the quarter-final at Al Janoub Stadium on Friday night (Saturday AEDT).
South Korean players begin to celebrate after winning the shoot-out against a dejected Saudi Arabia. (AP PHOTO)
Saudi manager Roberto Mancini walked up the tunnel with his back to play before Hwang Hee-chan buried the winning spot-kick, indicating his future, already under pressure, is in doubt.
The clash, played in front of a massively pro-Saudi crowd of 42,389 at Education City Stadium in Doha had been the most hotly-anticipated clash in the round of 16.
South Korea star Son Heung-min had some early half-chances but it was Saudi Arabia who came agonisingly close to opening the scoring in the 41st minute.
Saleh Al-Shehri cannoned a close-range header into the bar and a looping follow-up header from Ali Lajami rattled it again.
Then Salem Al-Dawsari headed it just past the far post, with aid from a South Korean deflection.
Saudi Arabia forward Abdullah Radif came off the bench at half-time and scored with his first involvement a minute later.
South Korea hardly fired a shot until the closing minutes, when they started to pepper the Saudi goal.
Klinsmann's charges broke through in the ninth minute of second-half injury time, with Cho Gue-sung's header forcing the match to extra time.
Both teams spurned chances in extra-time to win the game but mulleted goalkeeper Jo Hyeon-woo stood tall in the shootout, denying Sami Al-Najei, then Abdulrahman Ghareeb.
South Korea's goalkeeper Jo Hyeon-woo saves from Saudi Arabia's Abdulrahman Ghareeb in the shootout. (AP PHOTO)
All four of South Korea's penalty takers scored.
Australia have played South Korea 30 times, winning 11, drawing 11 and losing eight.
Most memorably, that included the 2015 Asian Cup triumph under Ange Postecoglou.
But since Arnold took the reins in 2018, they have gone winless in their two encounters.
Australia drew 1-1 with South Korea in Brisbane in November 2018 and lost 1-0 in another friendly in Busan in June 2019.
The winner of the quarter-final will face either Tajikistan or Jordan.
In Tuesday's other last-16 tie Uzbekistan beat Thailand 2-1 and will meet hosts Qatar.Â
Uzbekistan took the lead in the first half when Azizbek Turgunboev volleyed it past Patiwat Khammai.
Thailand equalised just before the hour mark through Supachok Sarachat's 25-yard shot. But seven minutes later Abbosbek Fayzullaev fired in a low shot from the edge of the box.
