With just one point from two games, Greece looked rank outsiders to progress from Group A at the start of play, but Giorgos Karagounis' strike in first-half injury time proved decisive.
Incredibly, Russia, who looked so good in their opening 4-1 win over the Czech Republic, will take no further part in the competition.
Russia was widely expected to comfortably secure at least the point they needed to secure their passage to the quarter-finals. And there was little early on to suggest that events in at Poland's National Stadium would divert from the expected script.
Dick Advocaat's side had the bulk of the possession and efforts on goal in the first period, although Greece was largely doing well to deny the opposition clear-cut chances on back-up goalkeeper, Michalis Sifakis' goal.
Andrey Arhsavin had one of the best opportunities as he met Alan Dzagoev's right-wing cross, but could only direct his close-range effort straight at Sifakis.
Alexander Kerzhakov continued his unfortunate streak in front of goal continued with a fine effort from the edge of the box that went just past the post and bar. Left-back Yuri Zhirkov also threatened from distance, but his effort soared inches over the bar.
With the half-time whistle just seconds away, what should have been a simple headed clearance from Sergei Ignashevich off of a Greek throw-in on the right turned into anything but. The experienced center-back committed a cardinal sin with a terrible square header that put Karagounis clean through down the inside right and the veteran playmaker made no mistake, drilling a low shot just to the side of Vyacheslav Malafeev.
The goal being especially special for Karagounis, coming as it did on the day that he equalled his country's appearance record, with 120 caps.
In the second-half, Russia appeared stunned at what had transpired at the end of the opening period and struggled to restore their dominance of the opening period.
Indeed it was Greece who should have had the chance to extend their lead. Karagounis was again to the fore using his trickery to get through in the area before tumbling under the challenge of Ignashevich. But rather than giving a penalty, referee Jonas Eriksson instead booked the Greek for diving. Karagounis looked on in disbelief as the yellow card emerged that meant that he would not miss his side's last eight encounter.
Greece came even closer to adding a second, 20 minutes from time, as a fine long-range free-kick from Giorgios Tzavellas cannoned back off the cross-bar, with Malafeev motionless.
Russia's best and last chance to get a vital equalizer came as Arshavin crossed in from right, but Dzagoev failed to score his fourth goal of the tournament as he put his header fractionally wide of the far post.
But incredibly, despite being undeniably the class of Group A, Russia are heading home and a Greek side that can just never be written off are looking forward to a quarter-final.