The Czechs were 2-0 to the good inside just six minutes as midfielders Jiracek and Pilar made the most of some generous Greek defending. Substitute Theofanis Gekas pulled a goal back after a terrible error by Petr Cech, but Fernando Santos' side lacked the guile to carve out an equaliser.
The Czechs' opening 4-1 loss to Russia left them knowing another defeat would end their hopes of reaching the last eight, but they could hardly have wished for a better opening. Jiracek put them ahead in the third minute as he ran onto Tomas Hubschman's pass to fire home, despite Greek goalkeeper Kostas Chalkias getting a hand to his left-footed shot.
Chalkias was then at fault for the second goal as he failed to cut out Theodor Gebre Selassie's low cross to allow Pilar to tap in his second goal of the tournament. The lively Pilar came close to adding a third as he played a neat one-two on the edge of the area before firing just wide of the left-hand post.
Georgios Samaras had Greece's first sight of goal but the Celtic striker made a mess of meeting Vasilis Torosidis' cross. Chalkias' miserable day continued as he was forced off after just 21 minutes, having pulled up after playing a pass out to his defenders, with Michalis Sifakis coming on to replace him.
Czech captain Tomas Rosicky was booked after his high boot caught his Greece counterpart Georgios Karagounis on the head but the Czechs' dominance continued as Sifakis was forced into his first save by a low Rosicky drive.
Greece thought they had pulled a goal back five minutes before the break as Georgios Fotakis headed in a Torosidis cross, but he was ruled to have been offside.
It should have been 3-0 seconds after the restart as the Czechs, whose captain Rosicky was replaced by Daniel Kolar at the break, again surged forward. Gebre Selassie found more joy down the right but Milan Baros could not get the ball out of his feet when just ten yards out.
Greece battle back
But it was the Greeks who found the net next thanks to a calamitous mistake from Cech. The Chelsea goalkeeper came racing out for an aimless long ball but, distracted by Tomas Sivok, he lost control and substitute Gekas had the simple task of directing the loose ball into an empty net.
Buoyed by the goal, Greece finally began to exert some control on the game, with Karagounis and Samaras becoming increasingly prominent. But they struggled to create any genuine clear-cut chances, and struggled to test Cech after the Chelsea keeper's blunder, as the Czechs comfortably saw out the closing stages for a vital win.