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Guus Hiddink pays tribute to his team's performance
Roman Pavlyuchenko put Russia ahead only for Ruud van Nistelrooy to level late on to take the game into extra time.
But Dmitri Torbinski and Andrei Arshavin secured the win for Hiddink's side.
Arshavin put in an impressive and influential match-winning performance and, while Hiddink praised his star man, he also praised the Russia team.
"Arshavin did very well but needs the assistance of the others," he said. "But he did a big job.
"He has tremendous skills. He knows how to dribble at a defence. Defenders can run with him but they cannot really attack him. It is what nature gave him."
Netherlands were a shadow of the side that won each of their three group games, including wins over France and Italy.
And Hiddink added: "The Dutch were just dangerous at set pieces and it was a blow to concede the equaliser, but more of an achievement to win after conceding this goal.
"In extra time I told the players to go forward and look for a goal as they were as tired as we were. I also told them to have mental strength and they responded perfectly.
"We did not talk a lot about it in the preview of the game but we had just two days to recover and prepare after a tough Sweden match."