Euro 2012: Greece 1 Russia 0
The Greeks took the lead just before the halftime whistle when Giorgos Karagounis sent a low shot under Russia goalkeeper Vyacheslav Malafeev with the final touch of the first 45 minutes.
"The moments are pure magic for all of us. This is a great night for all Greeks," Karagounis said. "I thank God for living these moments. I cannot describe how I feel. It's so great."
The win put the Greeks into the next round, where they could face Germany in a politically charged match that would bring the financial crisis onto the field at Euro 2012.
"We are proud that we gave the people back home some joy and a break from their problems — even for a short while," Greece striker Georgios Samaras said. "We did very well defensively, but the will we had was the main thing. That stopped them from scoring goals.
"I'm not concerned with who we play next, it's just great to have done this."
Karagounis, playing his national record-equalling 120th international match, will miss the quarter finals after getting a yellow card for diving. The Greece captain thought he won a penalty when he made contact with Sergei Ignashevich in the area, but Swedish referee Jonas Eriksson instead booked him.
Russia had been the overwhelming favourites going into the match at the National Stadium, but they were again guilty of squandering chances. The Russians finished the match with 25 shots on goal, while Greece managed only five.
"We should have won by a wide margin tonight but we didn't. My compliments to Greece," Russia coach Dick Advocaat said. "A number of players weren't sharp enough to score."
The Russians became one of the tournament favourites with their 4-1 win over the Czech Republic in their opening match, but then drew with Poland and finally lost to Greece, snapping a 16-match unbeaten run.
"We did go forward, were very attacking. We played well, but you have to score goals," Advocaat said. "We did that in first game and despite all the possession today we didn't do that today."
Russian players dejectedly tramped off the field immediately after the final whistle, while Greece's euphoric players hugged one another and then celebrated with fans.
"What I'm feeling is overwhelming. I think we did deserve more, but it didn't happen," Malafeev said. "To concede that goal just before halftime was an awful feeling."
Earlier, Giorgos Tzavelas nearly gave Greece a two-goal cushion when he curled the free kick over the Russian wall in the 70th minute but saw the ball slam against the top of the post. And Michalis Sifakis then ensured his team would advance when he saved a close-range shot by substitute Pavel Pogrebnyak in second-half injury time.
Russia came close several times in the first half, but even as the team laid siege to the Greek goal they were largely restricted to long-range efforts after the break as they went after the equalizer.
Russia forward Alan Dzagoyev came close in the 84th minute with a glancing header off a cross from Andrei Arshavin, but the ball drifted just wide.
Greece, knowing they needed a win to progress after a draw and a loss in their first two Euro 2012 matches, started the match with a defensive set up aimed at stifling Russia's passing game in the midfield. Russia only needed a draw to reach the quarter finals.
As the minutes faded away, the Greek fans sang the national anthem and the Russians lit flares and walked out of the stadium.