Greece earned a place in the knockout stage of Euro 2012 on Saturday with its only win in group play.
Now it hopes to replicate 2004, when it did the same thing in the group stage and won the title.
Giorgos Karagounis scored in first-half stoppage time as Greece downed Russia, 1-0, at National Stadium to rise from the bottom of Group A to second to seal a quarterfinal berth.
Russia fell from first to third on the final day of group play as the favorite to win the group was eliminated. Greece and Russia both ended with four points and the first tiebreaker was head-to-head play.
Czech Republic beat Poland, 1-0, on Saturday to win the group. Poland was also eliminated.
Greece will play the Group B winner Friday. Czech Republic will play the Group B runner-up Thursday.
Russia survived an early scare when Greece midfielder Kostas Katsouranis sent a pass into the 6-yard box that goalkeeper Vyatcheslav Malafeev had to deflect wide with Dimitris Salpingidis lurking at the far post.
Aleksandr Kerzhakov followed with a swerving side-volley from the edge of the area that just missed the top-right corner for Russia, and Yuri Zhirkov sent a rocket from outside the area just over the bar in the 40th.
Greece broke through in the second minute of stoppage time off a throw-in that was misplayed by Sergei Ignashevich. Karagounis took advantage to get behind the Russian defense, and slotted low to the far post to beat Malafeev.
Russia had its first good opportunity to even the match in the 57th when Denis Glushakov opened space outside the area, but fired wide from 25 yards.
Greece created the better chances over the next 15 minutes, with the first off a pass from Vassilis Torossidis into the 6-yard box for Theofanis Gekas that Russia defender Alexander Anyukov cleared from danger.
Karagounis had a penalty appeal denied in the 62nd, and was instead received a yellow card for a dive. Although Karagounis was upset by the call, Greece was able to produce another chance as Giorgos Tzavellas drilled the corner of the post and bar off a free kick in the 70th.
Moments later, the Czech Republic scored against Poland to leave Russia on the brink of elimination and Dick Advocaat called for striker Pavel Pogrebnyak off the bench.
Russia heaped the pressure on with its tournament on the line, and one chance came from Igor Denisov in the 75th when he forced a diving save from Greece goalie Michalis Sifakis.
Advocaat, who brought on Roman Pavlyuchenko to start the second half, used his final sub to bring Marat Izmailov on in the 81st, as he added another attacker to the field.
Alan Dzagoev, who scored three goals over Russia's first two games, directed a pass from Andrei Arshavin just inches wide in the 84th and Roman Shirokov sent a header on target in the 90th that was easily saved.
Russia needed just a draw to advance to the quarterfinals, but Greece held on for the improbable win - just its second in 12 games all-time in Euro finals - to pull off the upset and advance to the final eight.