Teemu Selanne scored an early goal and Tuukka Rask made 37 saves as Finland crushed the Russians' dreams of winning hockey gold in front of their own fans. Russian teams have won eight gold medals in hockey, but none in the last 22 years.
Selanne and Mikael Granlund each had a goal and an assist for the steady Finns, who overcame an early deficit and silenced the Bolshoy Ice Dome with two goals in the first period.
Despite its roster of high-priced offensive stars, Russia couldn't score in the final 52 minutes after Ilya Kovalchuk's early power-play goal.
Finland will face top-seeded Sweden in the semifinals on Friday.
Russia has failed to win a medal in three straight Olympics since 2002, and even home-ice advantage couldn't end the embarrassing drought.
A quarter-final exit is excruciating for the proud Russian team, which pressed relentlessly and fruitlessly in the third period after falling behind by two goals.
After the final buzzer, several Russian players stood on the ice with their hands on their knees. Evgeni Malkin, who failed to score a goal in the last four games, dropped to one knee before captain Pavel Datsyuk led the traditional post-game handshake line.
The Russians then gathered at centre ice amid more jeers and whistles than cheers, mournfully raising their sticks to salute the fans before skating off the ice at an arena built to herald Russia's return to hockey dominance.
Alex Ovechkin, the reigning NHL MVP and one of the Sochi Games' most public faces, failed to score another goal for Russia after scoring on his first shot just 1:17 into Russia's opener against Slovenia. Malkin, the Russians' other former NHL MVP, also didn't score a goal after the first four minutes of the opener.
Ovechkin, Malkin and Datsyuk all hailed Russia's home Olympics as the most important tournament of their careers, but they'll likely have only bitter memories.
Russia didn't play horribly in Sochi, winning three of its five games, but lost a painful eight-round shootout to the U.S. team before falling behind early and failing to catch up against steady Finland.
Semyon Varlamov allowed all three goals on 15 shots against the Finns before getting pulled for Sergei Bobrovsky during the second period.
Juhamatti Aaltonen scored the first goal for Finland, the most consistently successful Olympic team in the last two decades, winning medals in four of the past five games.
Russian fans realized the importance and peril of this game, filling the Olympic park early in the afternoon with cheers, chants and Russian flags. The Bolshoy crowd began chanting "Ro-ssi-ya!" even before pre-game warm-ups, waving hundreds of flags and banners emblazoned with hometowns and slogans.
The tone was uncommonly intense from the opening faceoff. After Granlund took an early holding penalty in the offensive zone, captain Pavel Datsyuk fed Kovalchuk for a hard shot over Rask's shoulder. Kovalchuk popped the water bottle off the top of Finland's net and celebrated with a two-footed leap into the air amid ecstatic cheers.
But moments later, Aaltonen made a beautiful move along the goal line, putting a shot under Varlamov's glove arm for the KHL forward's first goal in Sochi.
Bolshoy got quiet, and it became positively funeral-like late in the period when Granlund moved up the boards, broke past two defencemen and fed Selanne for the Finn captain's 22nd goal in a record-tying six trips to the Olympics. The 43-year-old Selanne extended his own record for the oldest player to score in an Olympics.
Finland scored again on the power play early in the second, with Granlund collecting Selanne's rebound and sliding in a backhand from a sharp angle. Granlund, who turns 22 in a week, hadn't been born when Selanne played in his first Olympics in 1992.
Russia put together an impressive offensive stretch after Bobrovsky came on, with Rask forced to make a big save on Alexander Semin's breakaway. The Russians continued to press in the third period, outshooting Finland 14-5, but Rask made big saves when his teammates didn't block Russia's shots.
Dozens of fans lingered in their seats long after the team left the ice, disconsolately folding their flags and staring at the ice. A few Finnish fans near centre ice even went up to a group of Russian fans for a hug.