Giorgos Karagounis scored the only goal as Greece produced a major shock to knock Russia out of Euro 2012 and seal their place in the quarter-finals.
Russia had dominated the game before Karagounis pounced on a Sergei Ignashevich error to drill in a shot.
Roman Shirokov had earlier been denied a penalty after claiming a push by Karagounis, who himself had a strong spot-kick shout waved away later on.
Giorgos Tzavellas struck the post with a free-kick as Greece secured victory.
Alan Dzagoev sent a late header wide from an Andrey Arshavin cross but Russia struggled to break down a resolute Greece and their first defeat in 17 games cost them dearly.
They finished on the same points in Group A as second-placed Greece but were eliminated because of their head-to-head record.
It was a remarkable turnaround for both sides as Russia had been tipped as potential tournament winners after beating the Czech Republic 4-1 in their opening game.
Greece, on the other hand, were given little chance of making it through to the last eight after winning a solitary point from their first two matches.
But the underdogs - who ground their way to unlikely Euro 2004 glory by relying on a stubborn defence and catching teams out on the counter-attack or with set-pieces - again managed to spring a big surprise.
They knew only a win against Russia would be enough to get into the quarter-finals and they started positively.
Kostas Katsouranis had a glanced shot from a Karagounis corner palmed away by keeper Vyacheslav Malafeev, and Vassilis Torossidis had a shot blocked.
But as the game progressed, the Greeks sat back, happy to soak up the pressure while trying to catch their opponents out on the break.
Dick Advocaat's Russia were allowed to pass and probe, quickly threatening as Arshavin's prodded shot was saved by keeper Michalis Sifakis.
Aleksandr Kerzakhov fired a sweet shot agonisingly wide before Shirokov was denied a penalty for what appeared a clear push by Karagounis.
A Zhirkov 22-yard shot went just over and Russia's failure to convert their domination into goals was punished by an unlikely goal for Greece.
Russian defender Ignashevich missed a headed clearance from a Greece throw-in and Karagounis, who was making a record-equalling 120th appearance for his country, raced clear before finishing with a great deal of composure.
The strike stunned Russia and Zhrikov was nutmegged by Torossidis, whose low cross was crucially intercepted by Aleksandr Anyukov with Fanis Gekas waiting to tap in.
Russia were now on the backfoot and Karagounis had strong claims for a penalty when he appeared to be tripped by Ignashevich.
Instead, referee Jonas Eriksson booked the Greece captain for diving, leaving Karagounis furious before being substituted.
The midfielder's frenzied protests almost had him tearing his hair out in despair as he also ran to the fourth official to complain.
His yellow card also means he will miss the quarter-final.
Russia, though, could not find the creativity to break down Greece and secure an equaliser.
Indeed Greece came closest to scoring when a Tzavellas effort struck the woodwork.
But Karagounis's solitary effort turned out to be decisive and Greece will now play the winners of Group B - who will be Germany, Denmark or Portugal.