Warsaw, Poland - Greece gave their troubled country a lift it desperately needed by stunning Russia 1-0 against the odds to reach the Euro 2012 quarter-finals on Saturday and send their opponents out of the tournament.Facing a tense election back home and mired in a deep financial crisis, Greece secured victory with a Giorgos Karagounis goal deep into first-half stoppage-time to put his side through as Group A runners-up.The Czech Republic, thrashed 4-1 by Russia in their opening game, beat Poland 1-0 to reach the last eight as group winners on six points.Greece and Russia, who could not repeat their impressive opening win which had commentators purring, were next with four, with Fernando Santos's side progressing thanks to the head-to-head rule.Greek players and coaching staff celebrated wildly on the pitch in front of their small section of fans who had been heavily outnumbered by the large Russian contingent that descended on the Polish capital.Greece stunned the football world by winning Euro 2004 as huge outsiders and could be on a roll again after the much maligned traits of being a well-organised, if limited side, proved a hurdle the more talented Russians, let down by wayward shooting, could not cross.Santos, the Portuguese coach charged with following 'King Otto' Rehhagel, the German who led Greece to triumph eight years ago, said his side had been inspired "by the history of Greece"."What we have achieved is very important," Santos, sitting with a Greece scarf draped around his neck, told a news conference."Greece has huge pride for its history. Everyone has to respect Greece."Russia, who had raised hopes of emulating their run to the semifinals four years ago, appeared to have their destiny in their own hands as they topped the group coming into the game.But despite the best promptings of Andrei Arshavin, their woeful finishing let them down and fate conspired against them elsewhere, with the Czech Republic's victory over the Poles ensuring it was the final match in charge of Russia for Dutch coach Dick Advocaat.Advocaat, heading back home to take charge of PSV Eindhoven, said his side were not sharp enough to score."Even though we lost today we played brilliantly in the first half," he said."Then they got a goal and that created a different story. "We didn't have the sharpness to score that goal."Russia had 25 shots to Greece's five and 62 percent of possession. But that counted for nothing as Greece, facing a win or bust game after taking just one point from two matches, took their chance when it mattered as the Russians fell asleep at the back.After withstanding long spells of pressure, Greece struck in the closing seconds of the opening half.Midfielder and captain Karagounis, winning his 120th cap to equal Theodor Zagorakis's record for his country, took advantage of poor marking at a throw-in to race into the box and fire hard past Vyacheslav Malafeyev.Victory and his goal were bittersweet for Karagounis who will be suspended for the quarterfinal after a second-half yellow card shown for diving, when the Greeks were convinced they should have been awarded a penalty."The moment is pure magic for all of us," Karagounis said. "This night is very important, it is something important for Greece for all Greeks. We said we would give it all, despite all the difficulties."We scored at exactly the moment we needed to. Now it is time to celebrate."The Greek party now heads to Gdansk and a quarterfinal showdown with the winners of Group B which Germany lead heading into the last round of matches.