Cam Fowler and Joe Pavelski scored in regulation for the Americans in the marquee game of the preliminary round. Jonathan Quick made 29 saves and stopped five attempts in the shootout.
International rules allow the same player to take multiple shots after the first three rounds of a shootout, and U.S. coach Dan Bylsma leaned on Oshie, one of the NHL's shootout specialists.
The St. Louis forward went 4 for 6 against Sergei Bobrovsky, ending the game with one last slow-developing move past the Columbus goalie. The Americans improved to 2-0 in preliminary-round play, all but wrapping up an automatic berth in the quarterfinals next week.
Captain Pavel Datsyuk scored two goals in regulation and another in the shootout for the Russians, who rallied from a third-period deficit. In a fast-paced game played in front of Russian President Vladimir Putin and an energized home crowd, the Russians also had an apparent goal waved off with 4:40 left because Quick's net came off its moorings.
The gimmicky shootout finish was entertaining, but the entire game at the Bolshoy Ice Dome was international hockey at its most compelling - and the third period was a thriller.
Pavelski scored the tiebreaking goal for the Americans on a power play with 10:33 to play, but Datsyuk tied it with 7:16 left during a Russian power play, spurring Putin out of his seat to cheer.
After review, the officials waved off Fedor Tyutin's apparent go-ahead goal because the net was loose, incensing the Russian crowd.
Both teams had quality scoring chances in overtime, but Bobrovsky denied Patrick Kane on a breakaway in the most hair-raising moment.
Oshie started off the shootout with a low shot between Bobrovsky's legs, and the next four shooters missed before Ilya Kovalchuk scored in the third round. Datsyuk and Kovalchuk scored in the fifth and sixth rounds, respectively, but Oshie tied it twice in dramatic fashion.
Datsyuk and Oshie both missed in the seventh, and Quick denied Kovalchuk again before Oshie ended it.
Oshie was among the final selections for the U.S. roster, and the 27-year-old from Warroad, Minn., was chosen for exactly this type of situation. Although Oshie has never had a 20-goal NHL season, the hard-nosed forward has one of the highest rates of shootout success among the American-born players.
Although the game had little impact on the medal race in Sochi, the finish woke up the echoes of a U.S.-Russia rivalry best known for the "Miracle on Ice" at Lake Placid in 1980, when a team of American college students stunned the Soviet Olympic team.
The sociopolitical impact of that game is long gone, and the nations have already met three previous times in the Olympics since NHL players joined the games in 1998. Several players on both teams are teammates in the NHL, and this result only helped determine positioning for next week's elimination games.
But the Sochi Games are extraordinarily important to the Russian players, and the arena was packed to overflowing with fans of both nations jovially posing for photos and comparing their colorful sweaters. The Russians waved hundreds of flags, blew horns and banged drums from the first moments of warm-ups.