In an enterprising but niggling clash that stirred memories of the teams' dramatic 2004 semi-final, decided in Greece's favour by a 'silver' extra time goal, Petr Jiracek and Vaclav Pilar struck in the opening six minutes for the Czechs.
But despite captain Tomas Rosicky's graceful conducting of the game from midfield against a shaky Greek defence, the Czechs failed to add a third and, following the diminutive maestro's halftime withdrawal with a heel injury, had to ride their luck in face of a spirited Greek fightback.
When substitute Fanis Gekas capitalised on an error by goalkeeper Petr Cech to pull one back in the 53rd minute, the prospect of a draw or worse loomed for the Czechs.
But they dug in, survived some torrid moments and secured a first victory over Greece in four attempts as an independent nation.
It was only the Greeks' second defeat in 23 games under Portuguese coach Fernando Santos, who succeeded 2004 hero Otto Rehaggel in 2010, but the loss of their first-choice central defensive pairing, through injury and suspension, left them vulnerable.
Watch from Skai (in Greek) - Ήττα με 1-2 για την εθνική Ελλάδας