Greece (18/1 to win Group B) made Nigeria pay for having a man sent off as they came from behind to win their Group B encounter 2-1.
Vassilis Torosidis netted a 71st minute winner to secure a first ever World Cup victory for the Greeks.
Kalu Uche had given Nigeria the lead from a free-kick, but after Sani Kaita was sent off, Greece drew level through Dimitris Sapingidis.
Nigeria can still qualify for the round of 16 if they beat South Korea in their final group game and Argentina see off Greece.
“We started the game well, controlled the game, got the goal and then had a sending off. That caused us problems, especially in the first half,” Nigeria coach Lars Lagerback said after the match.
“The positive thing is that if Argentina win their game we still have a chance to qualify,” Lagerback said.
Greece coach Otto Rehhagel was delighted with the outcome.
“We are going to take on Argentina, a world class team. They will clearly be better than us and we have got to see how to cope with them,” he said.
“We all know the Argentine team is of extraordinary quality.”
Nigeria struck first, on 16 minutes, when Uche’s free-kick eluded everyone including goalkeeper Alexandros Tzorvas.
But in the 33rd minute Kaita was red carded for foolishly kicking out at Torosidis.
Rehhagel reacted by replacing defensive midfielder Socratis Papastathopoulos with striker Giorgos Samaras, who minutes later had a shot cleared off the line.
Salpingidis found space to drive home his country’s first ever World Cup goal with a 44th minute strike that deflected off Nigeria midfielder Haruna Lukman.
Nigeria substitute Chinedu Obasi missed an open goal after a swift counter-attack, but Greece went close again through Samaras before Torosidis stabbed home a second after Enyeama had spilled a low Alexandros Tziolis shot.
Russian-based Kaita apologised after the match for the incident which turned the game.
“I apologise to everyone. To the Nigerian people, the officials and my team mates,” the 24-year-old said.
“I accept the red card as a justified decision, I am very disappointed, I hope Argentina can help us out,” Kaita added.
Nigeria forward Nwankwo Kanu remained typically relaxed about his country’s chances.
“If you look at the table it is not really bad, but we need a win,” he told reporters.
“We cannot go for a draw, we have to go all out and make sure that we win and then it depends on what happens between Argentina and Greece.”
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