Russia -- desperate to make amends for their dismal showing at the 2010 Vancouver Games -- took the lead in the quarter-final tie but three goals from the Finns sealed the host nation's fate.
The 3-1 loss was a second successive Olympic Games defeat at the last-eight stage for Russia, who were booed off the Bolshoi Ice Palace rink by their shell-shocked fans.
Teemu Selanne and Juhamatti Aaltonen scored first period goals for Finland after Ilya Kovalchuk had put Russia ahead, with Mikael Granlund adding the third.
"We are all crying and we are crying with you too. We are hoping for revenge. Maybe one day there will be revenge. But maybe not with this team," said the commentator on state television Channel One.
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Earlier Wednesday, Sweden thumped Slovenia 5-0. Defending champions Canada take on Latvia in the last eight while the USA will battle the Czech Republic.
The 29-year-old, who won combined gold at the 2006 Turin Games, did enough on his second ski to beat Frenchman Steve Missillier by nearly half a second in an overall time of 2min 45.29sec. French tyro Alexis Pinturault took bronze.
"This is the event I wanted the most," Ligety said. "This is the event I have been putting so much pressure on myself to win, so to pull through is an awesome feeling.