Hossam Abdelmaguid converted the decisive penalty as Egypt defeated Australia 4-2 from the spot to advance to the World Cup knockout round for the first time ever on Friday.
The match in Texas ended goalless through 120 minutes after a tightly contested encounter where both teams created chances but couldn't break the deadlock.
Egypt will now face Argentina, the tournament's defending champions, in the last 16, provided Lionel Messi's side avoid an upset against World Cup debutants Cape Verde.
Australia coach Tony Popovic made a bold switch before penalties, bringing in experienced goalkeeper Mathew Ryan as a last throw of the dice.
Harry Souttar's opening penalty sailed over the bar as the Socceroos stumbled immediately. The next five players from both teams all found the net, including Salah with a composed finish, before Australia's 18-year-old defender Lucas Herrington struck the woodwork.
Abdelmaguid stayed calm to slot home the winner, sending Salah into tears of celebration and breaking Australian hearts.
Emam Ashour had put Egypt ahead with a powerful header in the 13th minute at the Cowboys' stadium in Dallas. The early breakthrough forced Australia, who'd managed just two goals in their group matches, to take the game to their opponents in front of 70,000 fans.
Salah struggled to impose himself following a hamstring injury picked up in Egypt's previous game, leaving his team vulnerable at times.
Australia levelled 10 minutes into the second half when Mohamed Hany deflected the ball past his own goalkeeper. Neither side had won a knockout match at a men's World Cup before, so both teams sensed the significance of the moment.
Cristian Volpato, who switched from Italy to Australia just before the tournament, nearly gave the Socceroos an early lead when he struck the crossbar inside five minutes.
Egypt looked shaky in defence during stretches, yet Ashour's header came against the run of play after Nestory Irankunda failed to mark him at the far post, with Karim Hafez delivering the cross.
The goal marked Egypt's second of the tournament following their 3-1 victory over New Zealand in the group phase.
Australia mustered their first real attempt on target 10 minutes before half-time when Aziz Behich's shot proved comfortable for goalkeeper Mostafa Shoubir to handle.
Shoubir's father, Ahmed, kept goal for Egypt at the 1990 World Cup, continuing the family legacy.
The 34-year-old Salah, hampered by his injury concern, made little mark on the opening 45 minutes in an often scrappy affair.
Jordan Bos, among the tournament's speediest wingers, took a heavy knock from Rabia's robust challenge and left the pitch at the interval, replaced by Kai Trewin in a setback for Popovic's plans.
Seconds after the restart, Omar Marmoush should have extended Egypt's lead from close range but slid his shot wide of goal.
