Emam Ashour headed Egypt in front early on from a recycled set piece, with the Africans the better side throughout the first half.
Mohamed Salah, Omar Marmoush and Ashour found space in behind Australia's back five as Egypt pushed forward with their front line.
Australia grew into the contest as the half wore on, pressing higher and asserting themselves more as the game progressed.
Their equaliser arrived when Mohamed Hany turned a free kick into his own net, with Aiden O'Neill supplying the delivery.
Egypt goalkeeper Ramy Rabia was denied a stoppage-time winner by a stunning save from Patrick Beach in the 94th minute, sending the match into extra time.
Salah grew increasingly influential as extra time wore on but could not force a breakthrough, leaving the tie to be settled by penalties.
Egypt had lost their previous four World Cup shoot-outs, and their nerves were tested further when Australia manager Tony Popovic replaced Beach with Mathew Ryan for the shoot-out.
Ryan could not save a single Egyptian penalty, with Salah dinking his effort down the middle.
Harry Souttar and Lucas Herrington both missed for Australia, sending Egypt through 4-2 on penalties and into a last-16 meeting with either Argentina or Cape Verde.
Salah, who had recovered from a hamstring injury in the buildup, reflected on the significance of the achievement afterwards.
“Today was one of the best days of my life, making history with my country. I tried to give my best and play when I’m hurt because this is what I do for the country.
“I’m proud of the boys … I always tell the boys, just enjoy the moment. We can’t take it for granted. I don’t know how many times we’ve qualified for the World Cup and never before have we qualified from the group stage and now we’ve qualified for the next round. It’s a moment to enjoy.”
Egypt midfielder Haissem Hassan described the physical test Australia posed throughout the contest.
“We started well, taking the lead, and then they equalised. We knew it was going to be a tough match because they’re a very physical team, with a lot of endurance, and players who are very quick and powerful. We knew that at free-kicks and corners it was going to be difficult because they’re very big.”
“Honestly, it's incredible, because you know that in Egypt there are 120 million people you've made happy today, and you know that today there will be celebrations across the whole country… For every player, when you’re a boy, you dream of ending up like this.”
For Australia, there was pride despite the exit.
Awer Mabil said: “Obviously we should be very proud of what we have done as a nation this tournament. I think it's been a great tournament for us all as a country, and then also to showcase our young talent, also I think has been a great platform for the young ones to step up — and they have done that. So I think there's a lot to take away from it.”
Australia's run ends at the last-32 stage, but Mabil's comments pointed to a wider sense of progress for a squad built around emerging talent.
Egypt, by contrast, move on to face knockout football few had expected them to reach, with Salah insisting the achievement should be savoured rather than taken for granted.