Argentina are facing the prospect of an early World Cup exit after a dreadful error from goalkeeper Willy Caballero set Croatia on their way to victory and a place in the last 16.
On a night when so much was expected of Argentina captain Lionel Messi, Caballero made the most telling contribution to his team's fate with an attempted chip over Ante Rebic that backfired badly, allowing the striker to volley into an exposed net in the 53rd minute during Thursday's game.
Messi - adrift for much of the match, especially during a pedestrian opening half - rallied his side, but neither he nor substitute forwards Gonzalo Higuain and Pablo Dybala could find a way through in Nizhny Novgorod.
The closest Messi came was a half-chance, a snatch at a rebound from a Maximiliano Meza shot which was blocked by Ivan Rakitic and turned behind to safety.
It was a dogged defensive second-half display from Croatia, illuminated by a moment of magic from their own masterful number 10, Luka Modric.
His curled shot from range drifted beautifully beyond Caballero's gloves to put his side two ahead, before Rakitic's injury-time tap-in sealed a victory that moves the Europeans through to the knockout stage and also leaves them in a strong position to win the group.
Argentina are no longer in control of their own destiny. This defeat follows their opening 1-1 draw with Iceland, in which Messi missed a penalty, and now even a heavy win over Nigeria in their final game on Tuesday may not be enough to send them through to the next round.
Should Iceland beat Nigeria in their second Group D game on Friday, Iceland would need only a draw against Croatia in their final match.
For Messi, a prolific performer at club level with Barcelona, this was another harrowing chapter in his recent history of pain and disappointment in the international game.