Jiracek shot the ball past Greece goalkeeper Costas Chalkias in the third minute after a pass from Tomas Hubschmann sliced through the Greek defense. Three minutes later, Pilar scored his second goal of the tournament, beating Greek defenders to a ball sent across the goal by Czech Republic defender Theodor Gebre Selassie.
"This was a big goal for me, and it's great for the team," Pilar said. "I went in very hard in to meet Gebre Selassie's cross and got to the ball with my knee."
Substitute Fanis Gekas pulled one back for Greece in 53rd minute with a tap in after Chelsea goalkeeper Petr Cech spilled the ball and bumped into defender Tomas Sivok.
The result put the Czech Republic's bid to qualify for the quarterfinals back on track after an opening 4-1 loss to Russia in Group A. It was a setback for Greek hopes, however, after a 1-1 draw with co-host Poland.
The Greeks, who played without two key central defenders, nearly scored another in the 41st, but the header from Giorgos Fotakis was ruled out for offside.
"We conceded a silly goal and that gave the Greeks hope but we fought well and kept the victory," Czech Republic coach Michal Bilek said. "The Greeks really tried to score at the end, but our defense held very well."
Greece recovered well after its disastrous start, but lost another player when Chalkias limped off the field in the 23rd minute. He was replaced by Michalis Sifakis.
"This was another game with a very bad start for us," said Greece coach Fernando Santos, whose side had trailed after 17 minutes of the draw with Poland. "We were chasing the game for the whole match after going two down so quickly."
Despite the defensive problems, Santos stuck with his attacking lineup of three forwards. The strategy helped the Greeks dominate the second half.
Before Euro 2012, Greece's defense had been an important feature in its campaign to qualify, conceding just five goals in 10 games.
"We conceded so few goals in qualifying, and this happens to us," Santos said. "We did find our balance but could not get a second goal."
Czech Republic captain Tomas Rosicky came off with a foot injury in the second half.
The Czech fans booed coach Bilek at the start of the match, but the team soon rebounded from its defeat. The Czechs also avenged their semifinal loss to Greece at Euro 2004.
