Real Madrid star Modric then produced an electrifying 80th-minute goal before Messi's Barcelona team-mate Rakitic completed the scoring after Croatia sliced apart Argentina's hapless defence in injury time.
The defeat leaves the Argentinians facing an ignominious repeat of their 2002 campaign when they also went out at the group stage after being tipped as possible World Cup winners.
They could have taken the lead in the first half but Enzo Perez missed an open goal from just 12 yards in the 30th minute. It was Argentina's only shot in the first half -- and perhaps their best chance throughout the evening.
Croatia now go into the knock-out stages with two consecutive wins as Messi and Argentina's World Cup dream hang on a thread after the 3-0 rout on Thursday.
Here are the live updates:
Minute 90+1: GOAL!!!!!!!!!!!!! From the corner down the other end of the field, Rakitic, Kovacic and Mandzukic break down the middle of the park with a leisurely pace. It's Rakitic who puts the first shot on Caballero, saved by the keeper - but the ball deflects back to Kovacic who simply squares it back to the Barcelona man to score with ease. Its all over for Argentina.
Minute 84: Otamendi kicks Ivan Rakitic, gets into a brawl with the Croatian players. Gets a yellow. Frustration coming out in a wrong way.
Minute 82:Kovasic (in) comes in for Perisic (out)
Minute 73: Another defensive blunder by the Argentine side. The defence makes a complete mess after a Manduzic run into the box is deflected but not cleared.
Minute 71: Dybala has already started influencing the game within minutes of his introduction. He cuts in on the right flank and shots a curling ball towards the goal. Sails over the bar by inches.
Minute 63: Croatia survive and Argentina falter. In a well-worked move, Higuain is sent towards the byline on the left by Perez. He pulls it back for Meza who sidefoots towards the bottom left but Subasic pokes the ball out.
Minute 57: Change for Croatia. Kramaric comes in for Croatia's goalscorrer, Rebic. He walks off the pitch with injury.
Minute 56: Two changes for Argentina. Higuain comes in for Aguerro and Pavon comes in for Salvio.
Minute 51: Mercedo gets a yellow card after nastily hacking down Rebic.
Half-time report: Argentina fail to break the deadlock as a grinding first-half comes to a boring end. The game scattered with missed chances and nasty fouls saw both the teams miss genuine chances and open goal opportunities. The Argentina team look sloppy with their defending and the midfield lacks depth and creativity and will have to increase their work rate if they look to go home with three points.
Croatia's defence also look shaky, the midfield boosts of the likes of Modric and Rakitic but the team have failed to show any quality football in the first forty five minutes of game play. Argentina have controlled the maximum ball possession and also managed to create loopholes in the Croatian defence but the Latin American team have somehow failed to convert.
Both the teams seem to be in deep slumber in the first half and need to attack with renewed vigour in order to break the deadlock in the second half.
Minute 43: The game is getting physical as the first half comes to a boring end. Croatia fail to hold the midfiled play as Argentina maintain the maximum possession but both the teams fail to break the deadlock. two minutes of extra-time added.
Minute 39: Rebic makes a nasty foul. Gets Yellow. First yellow of the game.
Minute 37: Play is stopped as Mercado clashes with Rebic mid-air. Argentina wins a free-kick and play resumes with Argentina playing with 10-men
Minute 33: Mandzukic misses another golden opportunity. Vrsaljko delivers a wonderful cross in off the right wing and the striker can only land a glance with his diving header going wide of the near post.
Minute 30: What a miss by Perez! Meza fools Subasic and coaxes him out of his six yard area. Perez gets the deflected ball but shoots wide of an empty net!
Minute 24: Zlatco Dalic's tactic is to try and dominate the midfield, with his side looking to create their opportunities from wide positions. Argentina seem to press forward but both the teams fade out in the final third.
Minute 21: La Albiceleste may have the majority of possession (67 per cent) , but they are yet to translate that to clear-cut opportunities in front of the goal.
Minute 14: The match looks evenly balanced between the two teams with both the teams getting chances to score. Messi failed to connect a lobbed ball while Perisic's shot saved by Caballero.
Minute 12: Messi can't get the end of his foot on a chipped pass eight yards out from the Croatian goal. The ball goes safely into the hands of Subasic
Minute 7: Mandzukic steps on Otamendi as the two chase a ball in the Argentina half and the latter wins a free-kick.
Minute 4: Croatia makes the first attack with Ivan Perisic coming down the left flank and places a danfgerous low shot towards the goal. Willy Caballero clears it for corner.
Kick-off!
Line-ups out: Argentina has fielded a whole new starting XI as Mercado, Acuna, Perez comes in for Argentina and Marcos Rojo, Angel Di Maria and Lucas Biglia kept in the sidelines. Croatia, on the other hand, has made only one changes with Brozovic in for Kramaric.
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