Sergei Semak burst down the left and delivered a neat cross which Pavlyuchenko steered into the near post with Edwin van de Sar well beaten.
While the pretty open game looked sure to end in the Dutch's disappointment in 90 minutes, Rudd van Nisterolley came to rescue with four minutes remaining.
The Real Madrid striker headed in an unbelievable free-kick from Wesley Sneijder to send the game into extra time.
But Russians kept on the pressure and Arshavin held off the challenge from Andre Ooijer before clipping over a wonderful cross from the left which was tapped in by Torbinski, replacing Ivan Saenko in the 81st minute.
Arshavin then gave another dazzling performance as he turned and shot low into the corner after receiving a throw-in.
His effort took a deflection of Andre Ooijer before going through Edwin van der Sar's legs.
Both teams came out attacking but Hiddink's men seemed to settle down first with Yuri Zhirkov's free kick and forward Roman Pavlyuchenko's header both threatening a goal in opening minutes.
Russia's Den Kolodin tested the nerves of van de Sar by two consecutive spectacular long range drives from about 30 metres away.
Netherlands missed probably the best chance of the first half in the 29th minute when Rafael van der Vaart's calculated free kick whistled into the box.
With Ruud van Nistelrooy at the far post ready to tap in, the ball instead went past his outstretched foot and straight behind for a goal-kick.
Russian players celebrate the second goal in the quarterfinal against the Netherlands at the Euro 2008 Championships in Basel, Switzerland, on June 21, 2008.
Fans of the Netherlands look depressed after the team lost to Russia during the quarterfinal of the Euro 2008 Championships in Basel, Switzerland, on June 21, 2008. The Netherlands lost the match 1-3.
