The goal was scored by Martin Demichelis and Martin Palermo in the second half.
Otto Rehhagel's man were dominated for the majority of the match and tried to hit Argentina on the counter attack. The Albiceleste proved to be too strong though and eventually cruised to a comfortable win.
Maxi Rodriguez almost opened the score seconds before the half-time break when the Greek defence allowed him too much space inside the area. Tzorvas saved the winger's shot from close range though.
The loose ball was then picked up by the Argentinians again and Messi eventually won possession at the edge of the box. The Barcelona star tried his luck with a placed shot, but Tzorvas was once again on hand to deny the tricky forward.
Greece started the second half brilliantly and Samaras almost gifted his side the lead minutes after the break. Demichelis had slipped, leaving Samaras with a one-on-one against Burdisso. Samaras' initial shot was deflected, but he reached the ball first fired from a tight angle, and missed wide of the far post.
Demichelis finally broke the deadlock in the 79th minute after a corner kick. His first attempt was blocked by teammate Milito, but the error prone defender didn't waste any time to fire home the rebound from close range.
Messi then finally showed a flash of brilliance with five more minutes to go. The Barcelona star went by two opponents before beating the Greek glovesman with a good shot, only to see his shot hit the upright.
Veteran striker Martin Palermo added his name to the score sheet in the dying seconds of the game. Tzorvas was able to save Messi's shot from twenty yards out, but Palermo was alert to slot home the rebound.