Argentines take top spot in Group B
Argentina will play Mexico in the round of 16 on Sunday, while Greece has been eliminated.
"We are doing our duty. We are defending the Argentine jersey," Argentina coach Diego Maradona said. "Mexico is not going to be easy, a very difficult opponent. But we are calm and we are going to receive Mexico with all the respect Mexico deserves."
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Demichelis scored from short range in the 77th minute after his header bounced off teammate Diego Milito and back into his path. Palermo doubled the score in the 89th from a rebound after Greece goalkeeper Alexandros Tzorvas saved a shot by Lionel Messi.
Mnutes earlier, Messi's hard left-foot shot hit the near post.
"A well-deserved victory, no doubt about that," Greece coach Otto Rehhagel said. "We wanted to avoid an early goal, we managed to do that, but of course Argentina has more class and that earned them the win."
Maradona made seven changes to the lineup that beat South Korea 4-1 five days earlier. Captain Javier Mascherano and strikers Carlos Tevez and Gonzalo Higuain were all benched. However, Messi did start and he was given the captain's armband for the first time.
It made Messi, who turns 23 on Thursday, the youngest Argentina captain ever.
"That was something very special," Messi said. "I felt the constant support of my team mates. It was a beautiful experience."
Midfielder Juan Sebastian Veron returned after missing the previous game with a right-calf injury.
Only goalkeeper Sergio Romero, Demichelis, midfielder Maxi Rodriguez and Messi have been in on the team for all three of Argentina's games, ensuring the squad will be well rested for the round-of-16 clash with Mexico.
"They deserve a lot of respect," Maradona said of Mexico. "Even though they lost, they have their identity."
Although their game was less fluent than in previous matches, the two-time world champions dominated the match, espcially in the first half at the 45,000-capacity Peter Mokaba Stadium, where Argentina fans clearly outnumbered their Greek counterparts.
"My players played with their hearts and with excitement," said Rehhagel, who declined to comment on his own future as coach. "But it was just not enough to cause Argentina much troubles."
Argentina initially preferred to keep possession instead of pushing to create chances.
The first shot on goal came in the 18th minute when Sergio Aguero picked up a pass by Veron and dribbled past two Greece defenders before his left-foot shot forced Tzorvas into a diving save.
In the next minute, Tzorvas pushed the ball over the crossbar after a 30-meter (yard) attempt by Veron.
In the closing minutes of the first half, Maxi and Messi both saw their powerful shots blocked by the keeper.
"We knew that if we put pressure on Greece, they would finally make a mistake," Maradona said. "We did that very well."
Aguero, Veron and Messi were the most active players. Milito was well neutralized by Greece's five-man defense, while Sokratis Papastathopoulos committed several minor fouls while shadowing Messi and Georgios Samaras was a lonely striker up front.
Rehhagel had urged his players to produce the "match of their lives" to get a result against Argentina.
However, the 2004 European champions left their defensive tactics in the second half, which soon gave Samaras his team's first chance, though the Celtic striker shot just wide after entering the penalty area from the left wing.
Greece: Alexandros Tzorvas, Vangelis Moras, Alexandros Tziolis, Avraam Papadopoulos, Giorgos Karagounis (Nikos Spiropoulos, 46), Loukas Vyntra, Georgios Samaras, Vassilis Torosidis (Christos Patsatzoglou, 54), Sotirios Kyrgiakos, Sokratis Papastathopoulos, Costas Katsouranis (Sotiris Ninis, 54).
Argentina: Sergio Romero, Martin Demichelis, Clemente Rodriguez, Nicolas Burdisso, Mario Bolatti, Juan Sebastian Veron, Lionel Messi, Nicolas Otamendi, Sergio Aguero (Javier Pastore, 76), Diego Milito (Martin Palermo, 80), Maxi Rodriguez (Angel Di Maria, 63).