Eurosport - Tue, 22 Jun 21:23:00 2010
It took the tournament favourites 77 minutes to break down Otto Rehhagel's side who despite needing a point to have any chance of progressing were more intent on stifling their opponents.
The deadlock was broken as Martin Demichelis smashed the ball into the roof of the net.
The defender rose highest at a corner only for his first header to hit Diego Milito but he was in the right place to smash the rebound past Alexandros Tzorvas.
And substitute Martin Palermo added a second a minute from time after Lionel Messi skipped through the Greek defence.
Coach Diego Maradona made seven changes to the side that beat South Korea 4-1 five days ago with his side's progression to the last 16 all but secure.
Messi became Argentina's youngest World Cup captain as he led his country for the first time two days before his 23rd birthday but he was followed doggedly by man marker Socratis Papastathopoulos until coming alive in the closing stages.
Tzorvas made four decent first-half saves to keep Argentina at bay.
The Panathinaikos keeper turned Sergio Aguero's effort around the post after a lovely run and then tipped Juan Sebastian Veron's piledriver from distance over the top.
He also repelled a Maxi Rodriguez effort and pushed a Messi curler over the crossbar.
Tzorvas did make one mistake when he fumbled a cross but Aguero's goalbound shot was blocked by Loukas Vyntra.
It took 48 minutes for Greece to carve out a chance and it was a golden one. Georgios Samaras pulled off Demichelis and saw his first shot blocked by Nicolas Burdisso but it rebounded back to the Celtic frontman who pulled his second effort marginally past the far post.
Clemente Rodriguez had a 20-yard effort whistle wide but despite needing to score twice, Greece continued to keep men behind the ball and leave Samaras an isolated figure up front.
The sort of anti-football that became Greece's trademark in Euro 2004 continued to frustrate their opponents, Tzorvas pushing a Messi free-kick behind before holding Mario Bolatti's crisp half-volley.
But Greece have failed to keep a clean sheet in 2010 and they were undone as Demichelis netted just his second international goal.
With Messi finally released from his shackles, he began to shine, dancing past two players before unleashing a shot that came back off the inside of the post.
And he was the creator for Argentina's second as he beat two men and, although his first shot was saved by Tsorvas, 36-year-old Palermo was on hand to sidefoot home the rebound.
Palermo, who scored a crucial goal in qualifying against Peru after being overlooked by his country for 10 years, netted just nine minutes after coming on and Argentina can now look forward to a second round clash against Mexico on Sunday while Greece go home with a whimper.
Greece v Argentina
1st Half Goals 0-0
Shots on Target 3-10
Shots off Target 3-4
Blocked Shots 1-8
Yellow Cards 1-1
Red Cards 0-0
Passing Success 67.4%-91.1%
Tackles Success 80.8%-82.4%
Territorial Advantage 39.6%-60.4%