The Czechs scored both their goals within the opening six minutes thanks to some poor goalkeeping from Kostas Chalkias.
Their first goal arrived with just two minutes on the clock when Tomas Hubschman threaded a pass through for Petr Jiracek, whose left footed effort beat Chalkias despite the goalkeeper getting his hand to the ball.
Tomas Rosicky drilled wide from distance as the Czechs continued to control proceedings without creating much in the way of clear cut chances.
As the half drew to a close Giorgos Fotakis looked to have reduced the arrears when he headed in a cross from Vassilis Torossidis. However, the goal was ruled out for offside against the Greek attacker.
Greece came out after the restart with a greater attacking threat and within eight minutes they hauled themselves back into the match, albeit with a touch of good fortune.
The Greeks dominated the remainder of the match in terms of possession, but they rarely called Cech into any meaningful action as the Czech Republic held out to claim their first victory at Euro 2012.
The defeat is only Greece's second under the management of Fernando Santos, who took over in 2010.