Second half goals during the match on Thursday from Ante Rebic (53rd), Luka Modric (80th) and Ivan Rakitic (90+1) ensured Croatia stretched their winning run to two games after they breezed past Nigeria 2-0 in their opener.
Lionel Messi’s Argentina, who drew with minnows Iceland in their first game of the competition, will now have to depend on favours from other teams in their group after winning against Nigeria in their last engagement to harbour any hopes of advancing to the next stage.
The 2014 World Cup finalists have one point from two games while Croatia have six from two outings.
The game started with Croatia’s Ivan Perisic forcing Argentina goalkeeper Wilfredo Caballero’s into a low save for a corner in the 5th minute.
Messi nearly got on the end of a sumptuous lobbed ball into the box two minutes later, but his outstretched toe could not reach it with Croatia goalkeeper Danijel Subasic caught in no-man’s land.
Real Madrid midfield mainstay Luka Modric and FC Barcelona counterpart Ivan Rakitic combined well in midfield as the European outfit looked the better team in the opening exchanges.
For Argentina, Maximiliano Meza was found free in the middle of the box but his low shot was well-blocked by Dejan Lovren.
At the other end, Argentina’s relatively untested back three found their going difficult and on a couple of occasions almost paid the price for lack of communication.
Croatian defenders led by Liverpool’s Lovren too looked out of sorts on one occasion and it was due to their incoherence that the ball fell to Enzo Perez who had an empty net in front of him but hammered a shot into the side netting just before the half hour mark.
Mario Mandzukic had the best chance of the half when Sime Vrsaljko’s cross found the Juventus striker but 32-year old headed inches wide of target.
In first half stoppage time, Rebic also spurned a good chance from a super Modric through ball as both teams went into the break locked level.
Moments after the break, Gabriel Mercado received a yellow card for a tackle to stop Rebic from breaking through the midfield.
Sergio Aguero forced a save in the 53rd minute with a quick turn and shot from the left of the box.
Seconds later, Croatia were celebrating their opener after a Caballero blunder handed Rebic a golden chance.
The Chelsea keeper tried a chipped pass over Rebic but the ball fell to the winger, who volleyed over Caballero to give his side the lead.
Rebic came off with an injury soon after and Argentina fans whistled their disapproval when Aguero made way for Gonzalo Higuain in the 64th.
Meza’s shot at the near post was well-saved by Subasic as Argentina looked to equalise.
All their hopes, though, were dashed in the 80th minute when Real Madrid man Modric curled home a remarkable effort from outside the box.
Rakitic then completed the rout in second-half-stoppage time — the FC Barcelona midfielder passing past Caballero after the Argentine defence gave up on the play in their own box.