The Russians joined Slovenia, Latvia and the Czech Republic as winners Tuesday in a round of qualifying games that filled out the quarterfinals.
Slovenia opened the day with a 4-0 decision over Austria, Latvia surprised Switzerland 3-1 and the Czech Republic let almost all of a 4-0 lead get away before defeating Slovakia 5-3.
All of that action set up Wednesday's quarterfinal contests in which Sweden will meet Slovenia, Finland will play Russia, the United States will face the Czech Republic and Canada will take on Latvia.
During the three-game group play portion of the event every team knew it still had a chance for a medal even if it suffered a loss.
That all ended Tuesday with the four qualifying games in which a team had to win or go home.
The Russians had hoped to avoid having to play such a game this early, but they survived the pressure after taking part in consecutive contests that went into shootouts. Russia lost the first of those shootouts to the United States and then defeated Slovakia in the final group game.
Norwegian goaltender Lars Haugen was removed for an extra attacker with 2:30 to go in regulation and the Russians quickly responded with open-net goals from Radulov and Alexei Tereshenko.
Bobrovsky, who plays in the NHL with the Columbus Blue Jackets, was given the start despite suffering a loss in his only other appearance of these Olympics. He was in the Russian net when American T.J. Oshie scored four four times during six shootout tries to give the United States a 3-2 win.
Anze Kopitar of the Los Angeles Kings opened the scoring for Slovenia and Robert Kristan made 30 saves in the easy victory over Austria.
Latvia produced two goals in the first period against Swiss goalie Jonas Hiller, whose Anaheim Ducks had the best record in the NHL at the Olympic break. Latvia's Edgars Masalskis protected a 2-1 lead during the final 25 minutes of the contest until Lauris Darzins scored an empty-net goal with a minute to play.
The Czech Republic built a 4-0 lead through the first 36 minutes of its game, then gave up three goals to Slovakia in the second period -- two of them by Marian Hossa. It took an empty-net goal by Tomas Plekanec with 39 seconds to play to ease the pressure.