Argentina won their third straight game at the 2010 World Cup to top Group B and eliminate a Greek side that paid for their almost complete lack of ambition.
Greece coach Otto Rehhagel knew his team would probably require a victory to progress but he again stuck with the defensive tactics that he feels he must use if his side is to succeed against technically superior opponents.
His plan of keeping it tight against Argentina and striking on the counter-attack unravelled when Martin Demichelis smashed home the opening goal of a largely forgettable contest with 13 minutes left.
The Bayern Munich defender pounced after his initial header had struck Diego Milito and rebounded invitingly - and he crashed the ball into the roof of the net from the edge of the six-yard box.
Lionel Messi, skippering his side in the absence of the rested Javier Mascherano, had a frustrating evening as he received close attention from his opponents but he almost struck a second after a jinking run ended with a thunderous strike that crashed against the post.
But the second goal did come when another Messi strike was palmed into the path of substitute striker Martin Palermo, who slotted home with his right foot.
Exactly 24 years after scoring his infamous "Hand of God" goal against England at the 1986 World Cup, coach Diego Maradona, leapt for joy in his technical area.
His team will play Mexico on Sunday in the round of 16, with South Korea qualifying from second place in Group B.
But the legendary Argentine had cut a frustrated figure for most of the evening as his team dominated territory and possession but often struggled to break down well-organised opponents.
Sotirios Papastathopoulos man-marked Messi, following him faithfully all over the park as the Argentine skipper tried to find some space from which to exert an influence on the game.
It was a tactic that spoiled the contest as a spectacle but saw Rehhagel's team successfully reach the interval on level terms.
Argentina, with seven changes from the side that defeated South Korea 4-1, stroked the ball around with ease in the middle of the park but did not really threaten Tzorvas's goal until striker Sergio Aguero drew a save with a crisp strike from a wide position after 18 minutes.
Tzorvas tipped over long-range strikes from fit-again Juan Sebastian Veron and Messi, while Maxi Rodriguez was denied from 14 yards and Loukas Vyntra blocked from Diego Milito.
But as the opening half wore on there were signs that Greece's negativity, combined with their willingness to break up play by fouling the opposition, was starting to frustrate Argentina.
And there had been the occasional indication that Greece could trouble the Albiceleste's backline, with two long-range passes in particular catching Demichelis out of position.
Even so, Greece, who lost 4-0 to Argentina at the 1994 World Cup in a match that saw Maradona score his 34th and final international goal, had not mustered an effort at goal by the interval and the superb atmosphere at kick-off had waned considerably.
Unfortunately, the contest somehow managed to deteriorate further in the opening minutes of the second half, although Greece did at least get a shot at goal.
Demichelis again found himself isolated after another long ball towards Georgios Samaras, who looked set to pounce after a slip by the Bayern Munich defender but the Greek forward shot wide.
There was a continued lack of urgency to the contest, although virtually everything of worth came from Maradona's side, with Tzorvas palming a Messi free-kick around the post and saving a header from defensive midfielder Mario Bolatti.
For all Greece's defensive exploits they almost gifted their opponents a goal with a piece of comical defending when Tzorvas smashed a clearance into Vangelis Moras and was slightly fortunate to see the ball fly wide of his goal.
But after Argentina opened the scoring, the Greek side fell away.
Reflecting on their second World Cup campaign, they will have to be content with having registered their first World Cup win, having beaten Nigeria on Thursday.
Attempts on target
Attempts off target
Projected table based on current scores
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