Russia took a 1-0 lead into the final five minutes of regulation on Roman Pavluchenko's goal but Ruud van Nistelrooy scored in the 86th minute to force extra time.
Russia dominated the extra 30 minutes and went ahead in the 112th minute when Arshavin's relay was tapped in by Torbinski. Arshavin added an insurance goal five minutes later.
The Dutch entered the match after winning all three of its group stage matches by a combined 9-1 score, Russia will meet either Italy or Spain in the semifinals on Thursday.
2014: The Year in Music [PHOTOS]