It took one moment of madness from undisciplined Sani Kaita that resulted in a well-deserved red card for Nigeria’s Super “Chickens” to unravel to a more organized Greek side.
Kalu Uche put Nigeria in the lead with a well-struck freekick near the left corner of the penalty area that eluded everyone and crept in past a perplexed Alexandros Tzorvas.
But the Super Eagles' hopes took a major hit when Sani Kaita was sent off on 33 minutes after kicking out at Torosidis, the Nigerian leaving the pitch in tears.
As half-time approached Greece coach Otto Rehhagel threw on forward Georgios Samaras for defensive midfielder Sokratis Papastathopoulos as the Greeks, renowned for their defensive-minded play, seized the initiative.
The pressure paid off when Salpingidis netted Greece's first ever goal in a World Cup finals after his shot deflected into the net off Nigeria's Lukman Haruna to make it 1-1 at half-time.
Nigeria took off Peter Odemwingie for Chinedu Ogbuke Obasi at the beginning of the second half, which started in lively fashion with both sides threatening.
With less than 10 minutes gone in the second period the Africa side were forced into another substution when Uwa Echiejile replaced the injured Taye Taiwo.
As the second half wore on the game became stretched and in a dramatic spell Theofanis Gekas was denied by Nigerian goalkeeper Vincent Enyeama before Nigeria raced upfield with Yakubu Ayegbeni forcing Tzorvas into a smart save and Obasi missing a clear follow-up chance.
But minutes after pulling off a wonderful save Enyeama spilt a powerful shot by Alexandros Tziolis and Torosidis smashed in the rebound from close range, sealing the win.
Despite the defeat the Super Eagles retain a mathematical chance of reaching the knockout stages.