Petr Jiracek shot the ball past Greece goalkeeper Costas Chalkias in the third minute after a pass from Tomas Hubschmann sliced through the Greek defence. Three minutes later, Vaclav 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.
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.
"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 defence held very well."
The attack also played its part, with Pilar already emerging as a vital player for the Czechs.
"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."
The low point for his team came with Cech's second half blunder which allowed Greece back into the game.
"It was my mistake. Who else is there to blame?" the Chelsea goalkeeper said. "I'd been playing well till then, and I was determined I wouldn't let any in."
The Greeks, who played without two first-choice central defenders, had nearly scored in the 41st minute — but the header from Giorgos Fotakis was ruled out for offside.
Greece recovered well after its disastrous start, but lost another player when Chalkias limped off 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 defence 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 an achilles tendon injury in the second half, and team officials said it was too early to say whether it would rule him out for the Czechs' last group game against Poland.
The Czech fans booed coach Bilek at the start of the match, but the team soon rebounded from its previous defeat. The Czechs also avenged their semifinal loss to eventual champions Greece at Euro 2004.
Czech Republic: Petr Cech, Theodor Gebre Selassie, Tomas Sivok, Michal Kadlec, David Limbersky, Tomas Hubschman, Jaroslav Plasil, Petr Jiracek, Tomas Rosicky (Daniel Kolar, 46, Frantisek Rajtoral, 89), Vaclav Pilar, Milan Baros (Tomas Pekhart, 64).
Greece: Costas Chalkias (Michalis Sifakis, 23), Yiannis Maniatis, Kyriakos Papadopoulos, Vassilis Torosidis, Jose Holebas, Giorgos Karagounis, Giorgos Fotakis (Fanis Gekas, 46), Costas Katsouranis, Costas Fortounis (Costas Mitroglou, 71st), Georgios Samaras, Dimitris Salpingidis.