Jorge Sampaoli's side produced an abysmal second-half display that severely damages their hopes of following Croatia out of Group D, with Caballero's stray pass to Gabriel Mercado that was volleyed home by Ante Rebic in the 53rd minute proving the turning point.
Any hopes of a late Argentina fightback were extinguished 10 minutes from time as the irrepressible Luka Modric whipped a fine strike into the bottom-right corner from just outside the penalty area.
Argentina had all but given up by the closing stages and they were punished further in stoppage time when Ivan Rakitic tapped in from close range with barely a defender in sight.
All eyes were on Lionel Messi before the game after his saved penalty in the South Americans' opening 1-1 draw with Iceland and, once again, he was a shadow of the player that has starred for Barcelona.
Messi cut an isolated figure throughout and was unable to rouse his side in the closing stages, leaving them in danger of needing a win and a swing in goal difference to reach the knockout stages.
