Karagounis was the difference between the two sides. (AP)
Warsaw: There were echoes of Greece's Euro 2004-winning campaign as they advanced to the quarter-finals with a pragmatic display that ended in a 1-0 win over Russia, who suffered elimination as Czech Republic defeated co-hosts Poland in Group A's other game.
Despite being under pressure for large parts of the game the Greeks took the lead in first-half stoppage time as Giorgios Karagounis punished some sloppy defending. They remained resolute in defence throughout the second half to secure a famous victory.
The Ethniki came into the game knowing they needed a win to ensure qualification and they were the first to pull a save from the opposing keeper. Karagounis' near-post delivery was flicked on target by Kostas Katsouranis but a fully-stretched Vyacheslav Malafeev clawed the ball away.
Russia responded positively and three minutes later Alan Dzagoev broke in from the right following a quick throw. Andrey Arshavin got on the end of his cross 10 yards from goal and Michalis Sifakis was forced to parry the ball away.
Dick Advocaat's side were in the ascendancy and had two great chances to go ahead. Firstly, Aleksandr Kerzhakov failed in his quest to get his first shot of the tournament on target as his volley bent agonisingly wide of the far post. Then, moments later, Yury Zhirkov's cutback for Dzagoev was intercepted by Katsouranis.
By the half-hour mark the Russians had taken control of the match but were more often than not being restricted to shooting from range. Yet when in possession the Greeks lacked ambition and committed minimal numbers to their attacks.
Zhirkov fired over five minutes before the break but Fernando Santos' side held out and in stoppage time Karagounis fired Greece into a surprise lead. A misplaced header by Sergey Ignashevich was capitalised on by the 35-year-old who capped his 120th international appearance, equalling the country's all-time record, by surging into the area and slamming a low shot underneath Malafeev.
Roman Pavlyuchenko replaced the profligate Kerzhakov at half time but they continued to struggle against the resilient Ethniki defence. With space limited in the final third Igor Denisov plumped for an effort from distance only to see it swing wide.
Greece remained a threat on the counterattack and after Aleksandr Anyukov somehow cleared Vasilis Torosidis' cross away from inside the six-yard box, Karagounis received booking that will keep him out of the next match for diving in the area though it looked like a certain penalty.
Santos signalled his intent to see out the game with the solitary goal by replacing striker Theofanis Gekas with left-back Jose Holebas 25 minutes from time. But the Ethniki almost extended their lead in the 70th minute when Gergios Tzavellas' beautifully struck free kick rattled the frame of the goal.
In their desperation to find an equaliser Advocaat's side became extremely disjointed and another long-range attempt from Denisov was saved by Sifakis. With five minutes of normal time remaining Dzagoev came close to restoring parity but his header from Arshavin's cross shaded the outside of the post.
It is a result that turned Group A on its head, as despite having topped the group before the kick off Russia crashed out. The win for Czech Republic put them into the quarter-finals as group winners with Greece following them through in second position ahead of Russia and Poland.