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 half-time 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.
Santos drafted in Kyriakos Papadopoulos, just 19, alongside midfielder Kostas Katsouranis at the heart of the defence and the Czechs, thrashed 4-1 by Russia in their opening group game, smelt blood and produced a high-tempo start.
Tomas Hubschuman created the first with a neat through ball that Jiracek slotted in with a sharp left-foot shot and Rosicky made the second, his pass releasing Theodor Gebre Selassie whose low cross was bundled in by Pilar.
After failing to score in three games against the Greeks, the Czechs were pinching themselves, but Milan Baros, top-scorer at Euro 2008 with five goals, is now a pale imitation of his former pacy self and was unable to add to the opening salvo.
Greece lost their goalkeeper Kostas Halkias, at 38 the oldest player in the tournament and one of only three squad survivors from 2004, to injury but the Czechs allowed them back into the game and were lucky when a Giorgios Fotakis header was ruled fractionally offside before the interval.
Unperturbed, Greece attempted a repeat of the revival that brought a 1-1 draw with Poland in their opener, but despite substitute Gekas's tap-in when Cech floundered dealing with Giorgios Samaras's low cross, they only created panic on the pitch and tension around it as the Czechs battled through.
The relief, in a stadium packed with Czech fans, was overwhelming as the final whistle banished fears of a collapse to match their 2-3 loss to Turkey four years ago and erased some of the pain of Traianos Dellas's header in Portugal where the Greeks went on to become unexpected champions.
The Czechs, level on points with Russia at the top of the group, face Poland in their final group game in Wroclaw on Saturday when Greece meet Russia in Warsaw.
