BRATISLAVA, Slovakia -- Russia eliminated Olympic champion Canada 2-1 Thursday to reach the semifinals of the ice hockey world championships.
Russia will play Finland on Friday, and the Czech Republic will meet Sweden.
"It doesn't really matter for me who scores the goal," said Kovalchuk after his first goal at the worlds. "We just want to win. We showed some character.
"We need to recover tonight and it's going to be a big game tomorrow."
It was the first loss for Canada at this year's tournament while Russia lost to Germany, Finland and the Czech Republic in the group stage before reaching the playoffs.
"That's tough," Canada captain Rick Nash said. "It takes one game, one period, couple minutes here and there and you could be out of it.
"They got two goals, it was just a bad 10 minutes. It was unfortunate it was the last 10 minutes of the game."
Kaigorodov tied it midway through the final period with a short-handed goal, also on a breakaway. Kovalchuk, the star winger of the New Jersey Devils, won it with 7:41 remaining.
Canada started out strongly and had nine shots on goal in the first five minutes while Russia had none. Overall, Canada outshot Russia 37-20. But Russian goalie Konstantin Barulin was sensational with 36 saves.
Canada goalie Jonathan Bernier stopped 18 shots.
"It's not very good that two such big hockey nations meet in the quarterfinals because one of the two teams has to go home," Russia coach Vyacheslav Bykov said.
Russia topped Canada for the second straight year after winning 5-2 in the quarterfinals at last year's worlds. Russia, seeking its 26th world title, also beat Canada in the finals of 2008 and '09.
"We're happy to win and hope to keep it that way," Bykov said.
"Both teams played their hearts out," Canada coach Ken Hitchcock added. "We made a couple of mistakes in the third period ... we couldn't stretch the 1-0 lead once we had it. It was a very emotional and tense game. The difference in the game was at the end of the day some of the best players of Russia stepped it up in the third period when they needed to and played very well."
Jarkko Immonen scored twice to help Finland beat Norway 4-1.
"I don't think it matters for us [who we play next]," Finland captain Mikko Koivu said before learning it will be Russia. "We have to stay strong as a team, do the things that we do good, trying to do things that we can do better a little bit better again, and move forward."
After the scoreless opening period, Ken Andre Olimb gave the underdog Norwegians a surprising lead by converting a penalty shot 3:56 into the second.
But Immonen started the comeback with a slap shot to tie the game just 2 minutes later, and Tuomo Ruutu put the Finns ahead for good. Immonen added his second with another slap shot and Jani Lajunen completed the scoring.
Immonen is the top scorer at the worlds with seven goals. Ruutu has six.
Finland's first three goals came on power plays and the four-goal rally spanned just 12:28.
"Our goaltending was very good, penalty killing was excellent, and also our power play was very efficient," Finland coach Jukka Jalonen said.
Finnish goalie Petri Vehanen stopped 37 shots for the victory.
"Now we have a chance to play for the medals," Jalonen said.
Finland, the 1995 champion, last won a medal at the 2008 worlds when it took bronze.
Norway has never beaten Finland at the worlds.