Marseille forward Mamadou Niang gave the African visitors the lead with a neat finish in the 71st minute and substitute Guirane Ndaw's stunning free-kick doubled the advantage with 10 minutes left.
Greece, who qualified for the World Cup following a 1-0 aggregate victory over Ukraine in the European play-offs, struggled to make an impression in a disjointed display against their opponents, who failed to qualify for South Africa.
When the first sight of goal did come it was for the visitors in the 29th minute, with Remy Gomis playing in Niang with a superb through ball.
Greek keeper Alexandros Tzorvas was quick to come off his line, however, and the Panathinaikos man blocked Niang's shot brilliantly with his legs.
Greece finally awoke from their slumber after 37 minutes when Angelos Charisteas sent debutant Pantelis Kapetanos through down the right.
The 26-year-old Steaua Bucharest striker's low centre was just too strong for Giorgos Samaras, who failed to make contact as he slid in at full stretch.
The pattern did not change after half time, with Niang going testing replacement keeper Kostas Chalkias with two efforts in quick succession, first from a 64th-minute free-kick before blazing over from long range.
It proved an ominous sign as Niang broke the deadlock. The Marseille forward raced on to Demba Ba's pass before turning Liverpool defender Sotiris Kyrgiakos and slotting calmly into the bottom left corner.
Ndaw heaped more misery on the home team nine minutes later with a vicious free-kick from 20 metres which flew into the top left corner.
Chalkias then saved Greece from further embarrassment with a fine save from Birame Mame Diouf in the closing stages.
The Greeks will be hoping for an improvement when they continue their World Cup preparations with matches against North Korea on May 25 and Paraguay on June 2 before kicking off their World Cup campaign against South Korea on June 12.
