Veteran Greece coach Otto Rehhagel is living in hope his side can shock Argentina in their final Group B game and progress to the second phase of the World Cup.
A blunder by Nigeria goalkeeper Vincent Enyeama, curiously named man of the match, handed them a 2-1 victory at the Free State Stadium.
Enyeama, whose team were down to 10 men after Sani Kaita was dismissed with them leading 1-0, failed to deal with a soft shot from Alexandros Tziolis in the 72nd minute. The rebound fell to Vasileios Torosidis, who toe-poked home the winner.
It was a sad end for Nigeria who had opened the scoring through Kalu Uche's free-kick, only for Greece to equalise through Dimitrios Salpingidis.
But for the Greeks it marked their first win and first goals in five games in two World Cup finals.
Next up are Argentina on Tuesday and Rehhagel said: "They are a world class team, an exceptional side.
"It will be interesting to see how my team cope. I am just glad we have got a victory. It would have been a shame to have gone home without any points."
Nigeria struggled after Kaita's dismissal for a studs-up challenge on Torosidis and now face an early exit from the tournament.
While Kaita said sorry, coach Lars Lagerback hinted that Torosidis had play-acted.
Rehhagel responded: "I do not think our player was in any way responsible. You cannot say that."
Kaita said: "I would like to apologise to the Nigerian people, my team-mates and to the officials."
