كتب : Hatem Maher
Roman Pavlyuchenko fired Russia ahead 11 minutes after the break but Ruud van Nistelrooy brought Holland level four minutes from time.
Russia outplayed Holland in both halves of extra time.
In the second period, two strikes from Dmitri Torbinski and the impressive Andrei Arshavin helped Russia claim a memorable victory.
They will face the winners of Sunday's semi-final between world champions Italy and Spain.
Many have expected that Holland would have the initiative, but Russia were the ones who had the better chances.
Pavlyuchenko came close to putting Russia in front after eight minutes when he was picked out by Arshavin's cross from the right.
However, despite being totally unmarked, Pavlyuchenko's free header went over the bar.
Holland struggled to break down Russia's compact defense. The Oranje's three forwards were not given much space upfront.
A superb save from Edwin van der Saar denied Arshavin in the 31st minute.
Deserved Opener
Arshavin, who produced a brilliant display in Russia's victory over Sweden, skipped past his marker inside the area before sending a low curling shot that was blocked by the diving Van der Saar.
Russia defender Denis Kolodin tried his luck from distance on two occasions. His first effort was smothered by Van der Saar while his second went just over the bar.
Pavlyuchenko stunned the Dutch team when he opened the scoring in the 56th minute.
Sergei Semak whipped in a cross from the left to the Spartak Moscow man, who got ahead of Joris Mathijsen to convert the ball with a precise left-footed shot.
Russia should have doubled their advantage on several occasions.
Pavlyuchenko capitalized on an error by Mathijsen and tried to loft the ball over Van der Saar but the Manchester United keeper found no difficulty in clawing the ball away.
Lively full-back Yuri Zhirkov also came close seven minutes from time but he opted to play the ball across the six-yard box instead of shooting goalwards. The ball was eventually cleared.
Russia were made to pay for the wasted opportunities three minutes later.
Wesley Sneijder's free-kick at the far post found Van Nistelrooy, who headed home past Igor Akinfeev.
Complete Domination
The match went into extra time, during which Russia demonstrated their superiority.
Pavlyuchenko hit the bar with a fierce drive in the 97th minute while Holland defenders failed to deal with Arshavin's mesmerizing skills.
Russia managed to restore their lead in the 112th minute when Arshavin sent a cross from the left that hit the bar before falling to Torbinski, who skillfully slotted home at the far post.
Arshavin turned from provider to scorer four minutes later to wrap up the victory. His low shot from inside the area deflected off a defender and went between Van der Saar legs.