Lionel Messi scored his first goal in a World Cup knockout round on his 1,000th career appearance to beat Diego Maradona's tournament tally for Argentina as they beat off a late Australia fightback to win 2-1 on Saturday and reach the quarter-finals.

Messi put Argentina ahead after 35 minutes with a coolly taken strike low into the corner for his 94th international goal to pass the great Maradona's eight World Cup goals, in a match where he was instrumental in almost every Argentine attack.

Julian Alvarez added a second near the hour mark after a howler by Australia keeper Mat Ryan to set up a mouth-watering last-eight clash next Friday with the Netherlands, who beat the United States 3-1 earlier on Saturday.

With nothing to lose, the Socceroos, chasing a first-World Cup quarter-final berth, pulled a goal back when Craig Goodwin's powerful shot was heading wide but took a huge deflection off Enzo Fernandez and flew into the net for an own-goal.

Messi spurned two clear chances late on but it was Australia substitute Garang Kuol who set hearts racing in the stadium when he found himself alone in the area and fired a shot on the turn in stoppage time that was brilliantly saved by Emi Martinez.

Messi admitted the final moments were tense.

"We're through, which is the important thing," he said.

"It was a tough game, a tough day. We had very little time to rest. We were tired. It was a very physical game. We're happy with this victory and another step forwards.

"We've taken another step and now another difficult one is coming."

Scrappy start

Argentina took a while to get into a match that started off scrappy, with Alejandro Gomez, Fernandez and Alvarez combining well but unable to break down a resolute defence.

Messi struggled to make his mark in the early exchanges and Australia had their best chance of the half when Harry Souttar, over two metres tall, climbed high to head down from a corner but his effort lacked power.

Lifted throughout by rapturous, overwhelmingly Argentine support that sang and bounced in unison on all sides of the Ahmad Bin Ali Stadium, Argentina pressed and finally made the breakthrough.

Alexis Mac Allister passed to Nicolas Otamendi just inside the area, who tapped it gently into the path of Messi to fire low beyond the reach of the outstretched Ryan.

Argentina came back from the interval hunting for more and got a second in the 57th minute when Ryan bungled a backpass under pressure from Rodrigo De Paul and was robbed of the ball by Alvarez who turned and fired home.

Australia refused to give up and launched a succession of attacks.

After Goodwin's deflected shot found the net, there was a real prospect of extra time in a stadium where the Socceroos had booked their World Cup place via a penalty shootout in an intercontinental playoff earlier this year.

Australia pushed forward relentlessly and nearly equalised when Aziz Behich darted into the area and was goalbound before a brilliant saving tackle by Lisandro Martinez.

Argentina looked dangerous late on as they battled for a third goal, with Lautaro Martinez firing wide before substitute Garang Kuol missed with seconds left in stoppage time.

"I just hope that everyone back in Australia really respects what we’ve done and are proud of us as well," said Australia coach Graham Arnold.

"We took it to them. I felt that we finished off well. We had a great chance at the end there to equalise. I’ve got to be very, very proud of the boys."