Jan Koller steered in a header to put the Czechs ahead in the 61st minute before Jaroslav Plasil slid in to add a second.
But in an amazing end to the winner-takes-all match, Arda Turan halved the deficit in the 75th minute before Nihat came to the party.
The Turkey captain drew the sides level in the 86th minute when he took advantage of a ghastly error by Czech goalkeeper Petr Cech to poke home into an empty net.
And the Villarreal striker sparked delirium among the Turkish fans when he curled home an unstoppable winner with two minutes remaining.
Though Turkish goalkeeper Volkan Demirel was red-carded for a push on Koller in the last minute, the Czechs could not equalise the scoring.
In another match the same day, Switzerland notched their first win at the European Championship finals when it least mattered by beating a second-string side from Euro 2008 quarter-finalists Portugal 2-0.
Hakan Yakin scored both goals, firing home in the 71st minute when he was set up by fellow striker Eren Derdiyok and then converting an 83rd minute penalty.
In Group B on June 16 Poland will take on Croatia and Austria play against Germany.
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