Hossam Abdelmaguid tucked away the winning penalty for Egypt after Australia, still chasing a first World Cup knockout win, missed two.
Earlier, Emam Ashour scored in the 13th minute for Egypt, before teammate Mohamed Hany became the first player with two own-goals in the same World Cup tournament, allowing Australia to even the score at 1-1.
It was a tense affair on Friday in which Egypt and their captain Mohamed Salah wasted the better chances had ended 1-1 after 120 minutes in Texas.
Lionel Messi’s Argentina loom next for Egypt, as long as the reigning champions avoid a massive upset against tournament debutants Cape Verde in their last-32 encounter.
The Pharaohs will celebrate anyway, having reached this stage of a World Cup for the first time ever.
Australia coach Tony Popovic threw on experienced goalkeeper Mathew Ryan for the penalty shootout in a last-gasp gamble.
Shooting towards the Egypt fans and whistles raining down, defender Harry Souttar blazed the first penalty over to put the Socceroos on the immediate back foot.
The next five players all scored, including Salah with the coolest of penalties, before 18-year-old Australia defender Lucas Herrington hit the bar.
Abdelmaguid kept his nerve to send Egypt through to leave Salah in tears of joy and break Australia hearts.
Emam Ashour had given seven-time African champions Egypt the lead from a header after 13 minutes at the air-conditioned home of the Dallas Cowboys.
The early goal put the onus on a shot-shy Australia, who scored only twice in the group phase, to attack in front of a crowd of 70,000.
With Salah mostly ineffective following injury in Egypt’s last game, the Socceroos equalised 10 minutes after half-time when Mohamed Hany headed into his own net.
