Argentina broke Greece's resistance 13 minutes from time through centre back Martin Demichelis who blasted the ball into the net after his header from a corner was partially blocked. Messi made the second goal for Martin Palermo who tucked away the rebound in the 89h minute after his skipper dribbled into the area and saw his shot parried by Alexandros Tzorvas.
In the other match, South Korea drew 2-2 in a tense Group B match with Nigeria to advance to the second round of the World Cup
Messi, who became Argentina's youngest World Cup captain two days short of his 23rd birthday, earlier had two efforts tipped away by Tzorvas who had a busy night.
The goalkeeper, who saved twice from Sergio Aguero in the first half, also stopped an effort from point-blank range by midfielder Mario Bolatti at a corner with 21 minutes to go.
Messi was kept in tight check by the man-marking of Socratis Papastathopoulos, and was rarely able to show off his skills.
Greece forward Giorgos Samaras had a good chance early in the second half on the left of the box but was wide of the far post with their first shot at goal after a sterile first half.
VERON EFFORT
After almost 20 minutes of midfield sparring from the kickoff, a deep pass from Juan Sebastian Veron sent Aguero through and his shot from the left was saved by Tzorvas.
The corner was cleared to Veron who shot from 30 metres with the keeper again alert enough to tipp the ball over the bar.
Just past the half-hour, Aguero was close again when he met a right-wing cross but his shot was blocked by Loukas Vyntra.
Samaras then put a low ball through to Kostas Katsouranis running down the middle but he failed to reach it.
Sergio Romero had to fist away a free kick from Greece captain Giorgos Karagounis then Tzorvas had to save sharply again from Maxi Rodriguez and Messi, with his first effort of the match, just before halftime.
It was left to Demichelis to put Argentina ahead with his late strike but Messi was to play a big part in their second when he fizzed a shot goalwards from the edge of the area and Palermo was on hand to covnert the rebound and seal victory.
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