Russia's Andrei Arshavin was the architect as they dumped Netherlands out of Euro 2008 after extra time.
Russia took the lead in normal time when Roman Pavlyuchenko volleyed home, only for Ruud van Nistelrooy to head in an 86th-minute leveller for the Dutch.
But the brilliant Arshavin tormented Netherlands throughout and he crossed for Dmitri Torbinski to prod home.
Arshavin then sealed a semi-final spot in the 116th minute as he ran through and fired low past Edwin van der Sar.
Russia almost had to play with 10 men in extra time after Denis Kolodin was sent off by Lubos Michel in stoppage time, only for the referee to reverse his decision after a chat with one of his assistants.
It was the first European Championship quarter-final that did not have to be decided by penalties after going into extra time and was just reward for another spellbinding performance from the young Russians and their destroyer-in-chief Arshavin.
It was a triumph too for Russia's Dutch coach Guus Hiddink and his side will now meet either Spain or Italy in Vienna on Thursday in the semi-finals.
From the start Russia settled better than their more-fancied opponents as the Dutch struggled to match the fluidity of their earlier Euro 2008 performances.
Hiddink's men found joy down the flanks, exposing full-backs Gio van Bronckhorst and Khalid Boulahrouz, with one fine cross headed over from eight yards by Pavlyuchenko.
After Van Nistelrooy somehow missed the ball completely three yards out from a free-kick, Russia really began to assert their authority.
The untouchable Arshavin danced past Andre Ooijer inside the Dutch box and curled a right-foot shot goalwards that Van der Sar had to tip away for a corner.
Twice in two minutes, Denis Kolodin hit right-foot piledrivers from 35 yards, the first forcing Van der Sar to tip over and the second flying inches over the bar.
Dutch coach Marco van Basten withdrew the ineffective Dirk Kuyt at the break for Robin van Persie to bolster their attacking threat and almost immediately he screwed a volley wide, before Russia took the lead.
Arshavin cleverly played in Sergei Semak down the left and his cross was expertly dispatched into the net by Pavlyuchenko.
It was the first time the Netherlands had been behind at Euro 2008 and as they began to pour forward in greater numbers, the Russians - matching the counter-attacking brilliance of their opponents from earlier in the tournament - began to pick them off.
A glorious move led to right-back Alexander Anyukov forcing Van der Sar to parry his shot and then Arshavin scampered away down the left and sent in a devilish cross that just evaded Ivan Saenko.
The Netherlands were pressing but were frustrated by a lack of quality, until with four minutes left they somehow hauled themselves level, Van Nistelrooy netting a poacher's classic by heading in Wesley Sneijder's free-kick.
As the clock ticked into injury time, Russia defender Kolodin was given an almighty repreive by referee Michel.
Booked for the second time and then sent off for a foul on Sneijder, one of Michel's assistants told him - perhaps wrongly - the Real Madrid midfielder had not kept the ball in play, so Kolodin was allowed to stay on the pitch.
Ruud van Nistelrooy (right) heads in Netherlands' late equaliser
Pavlyuchenko cannoned a shot against the crossbar and Arshavin weaved his magic way around two more tackles only for substitute Torbinski to shoot at Van der Sar.
They were denied a clear penalty when Yuri Zhirkov was fouled in the box by Johnny Heitinga but soon after Arshavin danced down the left, flighted a tantalising cross over Van der Sar and watched as Torbinski poked in.
Arshavin got the goal his sumptuous display deserved when he wrapped it up four minutes from time, latching on to a throw-in and firing past Van der Sar.
Holland: Van der Sar, Boulahrouz (Heitinga 54), Ooijer, Mathijsen, Van Bronckhorst, De Jong, Engelaar (Afellay 61), Kuyt (Van Persie 46), Van der Vaart, Sneijder, van Nistelrooy.
Subs Not Used: Timmer, Stekelenburg, De Zeeuw, Robben, Melchiot, Bouma, De Cler, Huntelaar, Vennegoor of Hesselink.
Booked: Boulahrouz, Van Persie, Van der Vaart.
Goals: Van Nistelrooy 86.
Russia: Akinfeev, Aniukov, Ignashevich, Kolodin, Zhirkov, Semak, Zyryanov, Semshov (Bilyaletdinov 69), Saenko (Torbinsky 81), Arshavin, Pavluchenko (Sychev 115).
Subs Not Used: Gabulov, Malafeev, Vasili Berezutsky, Yanbaev, Alexei Berezutsky, Adamov, Ivanov, Shirokov, Bystrov.
Booked: Kolodin, Zhirkov, Torbinsky.
Goals: Pavluchenko 56, Torbinsky 112, Arshavin 116.
Ref: Lubos Michel (Slovakia).