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Ante Rebic, the brilliant Luka Modric and Ivan Rakitic scored the goals that mean Croatia are safely through to the last-16.
Otamendi played the full 90 minutes, but Aguero was replaced by Gonzalo Higuain after 54 minutes.
The result leaves Argentina with just one point from their opening two matches, meaning even a heavy victory in their final match against Nigeria on Tuesday may not be enough to see them progress.
In Group C, Benjamin Mendy was an unused sub as France beat Peru 1-0 to qualify for the knock-out stages, with Kylian Mbappe scoring the decisive goal.
And Denmark and Australia drew 1-1. Christian Eriksen scored a fine goal to give the Danes an early lead – but Mile Jedinak’s penalty saw Australia earn a point.
Brazil's preparations for today's game against Costa Rica have suffered a blow with the news Danilo has suffered a thigh injury and is unavailable for selection. However, Ederson, Fernandinho and Gabriel Jesus are all fit and will be hoping to be in Tite's starting XI. You can see full coverage of that game on ITV, with kick off at 1pm.
Serbia play Switzerland in the other game in Group E. That’s the evening kick off, 7pm on BBC.
And Nigeria play Iceland Volgograd at 4pm, with live coverage on the BBC.
Denmark 1-1 Australia
France 1-0 Peru
Argentina 0-3 Croatia
Nigeria v Iceland 4pm (BBC)
Brazil v Costa Rica 1pm (ITV)
Serbia v Switzerland 7pm (BBC)
All the latest news, views and transfer rumours from across this morning's back pages
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The latest instalment of our World Cup A-Z feature