Argentina's chances of reaching the last 16 of the World Cup in Russia were plunged into grave peril as they suffered a chastening 3-0 defeat by Croatia on Thursday night.

With their star player Lionel Messi cutting a desolate figure, the South Americans were taken apart by the gifted European team whose midfield pair Luka Modric and Ivan Rakitic outshone their more feted rival.

Argentina's nightmare in Nizhny Novgorod began eight minutes into the second half when goalkeeper Willy Caballero horribly miscued an attempted pass, chipping the ball to Croatia forward Ante Rebic, who showed great technique to volley home.

(Caballero reacts after his blunder gifts Croatia the lead)[Getty/Kyodo]

The shock briefly inspired Argentina, with Messi trying to lead a revival, but Maximiliano Meza spurned their best chance before the brutal finale. With 10 minutes left Real Madrid maestro Modric curled in a wonderful shot from outside the box, then, with Argentina's defense all at sea in injury time, Rakitic slotted home.

Croatia guaranteed their place in the knockout stages but Argentina, who drew 1-1 with Iceland in their first match, must now win their final Group D game against Nigeria and hope other results go their way.

"We played a perfect game which is what you need against a top side," captain Modric said, before adding, "Let's not be euphoric or get ahead of ourselves. Of course this win will boost our confidence, but let's keep our feet firmly on the ground."

(Maximum points from two games have put Croatia into the next round) 

In the first game of the day, Australia kept their hopes of reaching the knockout stage alive with a 1-1 draw against Denmark in Group C.

The Socceroos must now beat Peru, who can no longer progress after losing to France, in their final group game on Tuesday and hope the French defeat the Danes at the same time.

Australia fell behind in the seventh minute when Denmark's star man Christian Eriksen fired home a fierce half volley, after being set up by a sublime flick from Nicolai Jorgensen.

But Australia equalized in the 38th from a penalty awarded by the Video Assistant Referee after Mathew Leckie's header struck the hand of Yussuf Yurary Poulsen, the second spot kick he has conceded in the tournament.

Australia captain Mile Jedinak kept his cool in the face of Denmark keeper Kasper Schmeichel's attempts to distract him, and slotted in his second penalty of the tournament.(Mile Jedinak celebrates after pulling the Socceroos level)[Getty/Kyodo]

It was the 11th penalty of the tournament, one more than in the entire group phase in 2014.

Australia had the better of the second half, with Schmeichel saving well from Daniel Arzani and Leckie, and they will hope to be more clinical against Peru.

Having lost 2-1 to France in their first game on Saturday, defeat by Denmark would have left the Socceroos on the brink of becoming the second team from the Asian Football Confederation to be eliminated, after Saudi Arabia were sent packing on Wednesday.

"After two games we should have four points," said Australia coach Bert van Marwijk. "The first part of the game we were not convinced we could play against them, then they saw the solution and from then on we controlled the game and Denmark were afraid of us. We had chances to win and we deserved to win."

Australia striker Andrew Nabbout, who plays for Japanese club Urawa Reds, was substituted in the second half after suffering a serious shoulder injury. "I think the tournament is over for him," said van Marwijk.

France ensured their place in the round of 16 by edging Peru 1-0, 19-year-old Kylian Mbappe becoming his country's youngest ever World Cup scorer.

(Hero Mbappe (C) gets a hug from his teammates)

Despite Peru's irrepressible fans making the Ekaterinburg Arena seem like it had been relocated to Lima, France were much stronger in the first half and took the lead in the 34th minute.

Olivier Giroud's shot deflected off a Peru defender and over keeper Pedro Gallese for Mbappe to convert almost on the goal line.

Peru pushed hard for an equalizer in the second half, Pedro Aquino hitting the post with a 30-yard shot, but they did not quite have the guile to produce a leveler and there were more tears for the South Americans at the final whistle.