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.
Emam Ashour celebrates his goal. Photo / Photosport
With Salah mostly ineffective after injury in Egypt’s last game, the Socceroos equalised 10 minutes after half-time when Mohamed Hany headed into his own net.
Both sides sensed history, neither having won a knockout game before at a men’s World Cup, and they went to extra time after late Egypt pressure.
With nothing to divide them they went to penalties.
Popovic’s side had nearly taken the lead with less than five minutes gone as Cristian Volpato – who switched to Australia from Italy on the eve of the World Cup – rattled the top of the crossbar.
Egypt, who won a World Cup match for the first time in the group phase when they beat New Zealand 3-1, looked nervy at the back.
Slightly against the run of play, Hossam Hassan’s men took the lead.
Australia forward Nestory Irankunda failed to pick up Ashour, who headed home at the back post from a cross by Karim Hafez for his second goal of the tournament.
The Socceroos had their first shot on target 10 minutes before the break when full-back Aziz Behich fired tamely at goalkeeper Mostafa Shoubir.
His father, Ahmed, played in goal for Egypt at the 1990 World Cup.
The 34-year-old talisman Salah, who came into the match after a hamstring strain, made little impact in an attritional first 45 minutes.
The half ended with Jordan Bos, one of the fastest players at the tournament, in a heap after a robust flying challenge from Rabia.
The wing-back had to be helped from the pitch and was replaced at half-time by Kai Trewin in a blow to Australian hopes.
Seconds after the restart it should have been 2-0 when Egypt’s Manchester City attacker Omar Marmoush slid the ball off-target from close range.
Egypt’s coach had said he was wary of Australia’s physical approach, and so it proved as Hany headed under pressure into his own net from an in-swinging Socceroos free-kick.
It was Hany’s second own goal of the tournament.
Former Liverpool superstar Salah remained a peripheral figure but was involved in the build-up as Australian stopper Patrick Beach saved athletically deep in added time to keep out Ramy and force another 30 minutes.
Egypt finished normal time the stronger and Salah fired well over early in extra time on his weaker right foot, with penalties looking increasingly inevitable.
Salah though was to prove more reliable in the shootout as Egypt triumphed.
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