Greece skipper Giorgos Karagounis scored the solitary goal of the game when he bounded into the Russian box a couple of minutes into time added on in the first half to drive the ball under goalkeeper Vyacheslav Malafeev at the Polish capital's modernistic national stadium. It was an astonishingly sloppy piece of defending from a throw-in before the goal that ultimately cost the much-vaunted Russians their place at these finals.
Russia and Greece finished on four points behind Czech Republic, who topped the section on six points with their 1-0 win over eliminated co-hosts Poland, but it is Greece who progress on the head-to-head records between the two countries.
Greece unearthed a superb performance high on energy and organisation with the kind of defending that carried them to the Euro 2004 title under former coach Otto Rehhagel against all the odds in Portugal, but it would be wrong to label this a fortunate Hellenic success.
Greece were the more purposeful side in the second half and should have been awarded a penalty when Karagounis was somehow booked after appearing to be felled in the Russian area by Sergei Ignashevich around the hour-mark.
Karagounis was furious with the referee and will now miss a possible quarter-final against likely Group B winners Germany in Gdansk on Friday, but he had already contributed to the biggest upset of the tournament so far. He was replaced by Grigoris Makos on 67 minutes perhaps for his own good.
It could hardly detract from a special evening for Karagounis, who equalled Theodoros Zagorakis's national record for Greece in his 120th appearance. It is a pity that he will not be around for the quarter-finals having also missed the Euro 2004 final win over Portugal due to suspension.
Giorgios Tzavellas also whacked a free-kick off the bar from 25 yards out on 70 minutes as Greece attempted to put breathing space between themselves and the Russians, who looked dazed at full-time having gone into the match on the back of a 4-1 win over group winners Czech Republic and a 1-1 draw with Poland.
The Czechs top Group A, but Greece celebrated like they had won the tournament at full-time.
Russia dominated large swathes of possession, but came up short on the night with their inability to penetrate Greece all too obvious.
The Greeks had lost both of their previous meetings with Russia in the European Championships - 1-2 in Euro 2004 and 0-1 in Euro 2008 - but this was as good a time as any to end that record.
Malafeev was forced to tip away a Kostas Katsouranis volley in the opening moments before Russia decided to display their superior technical skills on the ball without ever ramming home the territorial advantage four years after they had cut a dash to the last four of Euro 2008.
The under-worked Greece goalkeeper Michail Sifakis saved from Andrei Arshavin on nine minutes, but had little to do as Alexander Kerzhakov - who was replaced by the equally impotent Roman Pavlyuchenko at half-time - and Yuri Zhirkov illustrated Russian profligacy by walloping efforts wide.
With the roaming Georgios Samaras producing some admirable work to carry Greece forward on the counter attack from time to time, they could easily have added to their tally with Alexander Anyukov nudging the ball away from under his own bar after some decent work and cross by the lively Vasilis Torosidis on 58 minutes.
Russia huffed and puffed, but could not find a way through the Greece wall of bodies as it became obvious the men in the white shirts were not willing to be breached. An Alan Dzagoev header that dropped wide from Arshavin's cross on 83 minutes was the last time they would come close to lancing the Greece goal.
It was a bitter pill to swallow for Russia coach Dick Advocaat, who departs the post to return to club football with PSV Eindhoven next month. It was difficult not to feel heartened by the scenes of joy emanating from the Greek fans.
With the well-publicised monetary problems in Greece all too apparent, this will be a real boost for a country addicted to the world game. They may be heading out of the Euro, but Greece are well and truly alive at the Euros.