Former Bayern Munich coach Rehhagel adopted defensive tactics to shackle Argentina's creative players in their final Group B match, employing defender Socrates Papaststhopoulos to man-mark Lionel Messi.
But Diego Maradona's side finally broke through when defender Martin Demichelis lashed home a loose ball from a corner in the 77th minute before Martin Palermo sealed the win one minute from time.
And Greece's fate was sealed when South Korea drew 2-2 with Nigeria, ensuring the 2002 semi-finalists took the second qualifying spot behind group winners Argentina.
"My players played with their hearts and with excitement," said Rehhagel after the Argentina game, although they were heavily criticised elsewhere for their perceived negativity.
Rehhagel's side lost their opener against South Korea 2-0 before raising hopes they might qualify for the knockout stages with a 2-1 victory over Nigeria, their first ever World Cup win.
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