Argentina and Croatia meet at the Nizhny Novgorod Stadium for the second round of fixtures in Group D.
Argentina face a serious threat of an early elimination from this year's World Cup, after defeat at the hands of Croatia.
The Eastern European side took the lead in a fortuitous fashion, with Willy Caballero slicing a clearance and Rebic was there to hit home a sublime volley.
Lionel Messi twice had the chance to equalise. In one case Gonzalo Higuain played him in for a close-range shot but Subasic saved it with his legs and in a second attempt, Ivan Rakitic made a superb block to deny his Barcelona teammate any glory.
With ten minutes to go, Croatia captain Luke Modric doubled his side's lead, powering home a superb effort past a despairing Caballero.
Argentina had a chance for consolation but Vida made a superb block to deny Meza a goal.
Croatia then scored their third, as Rakitic scored on the rebound having initially seen his effort saved.
It was a physical affair between the two sides — Argentina picked up a number of yellow cards, as their frustrations began to show.
Five takeaways from Argentina vs Croatia
Messi-mad Maradona appears again
Diego Maradona, who was seen at Argentina's last game, made an appearance once again. The footballing legend, also Argentina's former manager in 2010, was seen at the game holding Lionel Messi's training shirt as he kissed it, showing his admiration for the Barcelona legend.
Argentina's defeat came as no surprise given how loose they were on the ball — Caballero's error was evidence of how poorly organised the Argentina defence were.
From their defence to their attack, there was just no rhythm to Argentina's play today. Jorge Sampaoli will have a lot to answer for, having changed his tactics from the first game. The team's main stars like Lionel Messi, Gonzalo Higuain, Sergio Aguero and Pablo Dybala couldn't link up with one another.
Croatia blaze a trail to victory
After a shaky first-half performance, the Croatians sured themselves up and became defensively solid. They worked hard for all three goals and were fully deserving of their victory.
Other than one opportunity, which was superbly saved by Subasic, Lionel Messi failed to test the Croatian goalkeeper.