The holder was trailing 2-0 and 11 minutes from a shock defeat, but goals by Cristian Romero, Messi and two minutes into stoppage-time from Enzo Fernandez remarkably kept it in the competition.

Egypt had been on the brink of one of the great FIFA World Cup upsets after Yasser Ibrahim and Mostafa Zico scored excellent goals, one in each half, and Messi had squandered an early penalty.

The North African side fell apart in the closing stages, though, as the 39-year-old Messi, whose record FIFA World Cup goal haul is now up to 21, orchestrated Argentina's dramatic revival.

The captain provided the cross from which Romero headed home to start the comeback in the 79th minute and four minutes later Messi crashed home the equaliser after substitutes Lautaro Martinez and Gonzalo Montiel had both got vital touches to keep the ball away from Egypt defenders.

The winner came from a counter-attack as Lautaro Martinez crossed from the right and Fernandez cushioned a back-post header past goalkeeper Mostafa Shoubir.

"I'd been longing for this goal for three years. We have a phenomenal group, one that never gives up," Fernandez said.

"We had to take advantage of the spaces they gave us, and we did. We came here to enjoy another [FIFA] World Cup and to represent our country. And that's what we're doing."

Egypt felt it deserved a penalty before the breakaway and vociferously complained but to no avail.

It had been surprisingly attacking in the early stages, bucking a recent tendency of sitting back and looking for counter-attack opportunities, and it opened the scoring after 15 minutes.

Emam Ashour attempted to tease his way past the Argentina defence on the right flank but, seeing no way through, passed back to Marwan Attia, who floated in a long cross that Ibrahim rose to head home.

The lead should have only lasted four minutes as Haissem Hassan caught overlapping Argentine full back Nicolas Tagliafico with a late tackle to give away a penalty.

But it only served to mark the start of the goalkeeping heroics of Shoubir, whose dive to the left easily stopped a weak left-footed effort from Messi that was too close to the keeper.

Messi became the first player to miss two penalties at a FIFA World Cup after also failing from the spot against Austria in the group phase.

Shoubir made a reflex stop to deny a point-blank header from Alexis Mac Allister in the 28th minute, and pulled off an even more extraordinary save six minutes from half-time to stop Julian Alvarez’s shot, stretching to turn the ball around the post.

In between, Messi crashed a free-kick against the post.

Egypt had the ball in the net in the 62nd minute but Zico’s finish, after a sweeping move inspired by Hassan’s trickery and Mohamed Salah’s pass, was chalked off after a video assistant referee (VAR) review found that Attia had fouled Lisandro Martinez in the build-up.

Five minutes later, however, Egypt doubled its lead in similar circumstances. Salah swept the ball forward on the counter, Hassan took it to the byline, and Zico came storming in to finish the cutback pass.

"The win was within our reach. We were only missing a few small details," Shoubir said. "As everyone saw, we were close – very close – to winning but it just wasn't meant to be."

Argentina advances to a quarter-final against Colombia or Switzerland in Kansas City on Sunday (AEST).