Evgeni Malkin scored two goals to help Russia beat the Czech Republic 4-0, and Tony Martensson scored three in defending champion Sweden's 7-4 win over Slovakia. Russia, undefeated in seven games and bidding for its first title since 1993, will next play either the United States or Finland. Sweden will next face Canada or Switzerland.
"It's just an unbelievable atmosphere right now. We win the game and everyone supports us," Russia forward Alexander Ovechkin said. "We feel good and we can't wait for the next game."
The Czechs, who have four of the last eight titles, had reached the final at the last two championships, winning gold in 2005.
Andrei Markov gave Russia the lead in the first period and Malkin scored two of Russia's three goals in the final period. Alexander Eremenko made 27 saves to earn the shutout.
Alexander Frolov sent a backhand pass across the slot to Markov, who wristed it over Roman Cechmanek's right shoulder on the power play 6:48 into the opening period.
After a scoreless second period, Ilya Kovalchuk sent a slapshot from the circle that bounced off the end boards and onto Malkin's stick. The Pittsburgh Penguins forward put the rebound through an opening between Cechmanek's right foot and the post to make it 2-0 only 23 seconds into the final period.
Cechmanek later came out of his crease in a risky move and fell. Alexander Radulov took advantage of the scramble by sending a slap shot past the goalie, who had dropped his stick.
Malkin added the fourth goal on a breakaway. With Czech Republic defenseman Zbynek Michalek chasing, Malkin scored a wraparound goal with five minutes to go.
"I think they're the best team here," Czech Republic forward Tomas Plekanec said. "We were there for the first two periods but the second goal in the third period was huge for them and then we just didn't play."
Russia has scored a tournament-leading 39 goals this year.
No host country has won the worldchampionships since 1986, when the Soviet Union was undefeated in 10 games.
Marian Hossa scored for Slovakia 2:10 into the first period, and Richard Kapus added another at 8:16. Fredrik Warg kept the Swedes within one with a goal at 7:28.
Sweden rallied in the second, scoring three times. Jonathan Hedstrom scored one before and one after Martensson, making it 4-2.
"It was tough for us because they came out well and we had to struggle to get back in the game," Sweden defender Magnus Johansson said. "The equalizer in the second period was a big thing because we began to control the game."
In the third period, Branko Radivojevic pulled the Slovaks back within one, converting a rebound. But Martensson scored his second six minutes later and Johansson made it 6-3 for the Swedes on a two-man advantage two minutes after that.
Roman Kukumberg scored Slovakia's final goal, swiping in Radivojevic's mid-air pass over Slovakia goalie Karol Krizan with nine minutes left.
Slovakia later pulled Krizan for the extra attacker, but Martensson scored his third 15 seconds from the end.
"We knew they were going to play their game so we needed to make better decisions on the ice, which did not happen in the second period and they were able to score goals," Slovakia forward Miroslav Satan said.