Rick Nash scored his tournament-leading ninth goal in the last period to lead Canada past last-place Ukraine 2-1 in their second-round finale at the hockey world championship on Tuesday.
Canada will meet Slovakia in today's quarterfinals.
Unbeaten Russia will play Finland, and the US will face the Czech Republic in Vienna, while Sweden will oppose Switzerland in the other quarterfinal in Innsbruck.
Sweden, the runner-up in 2003 and 2004, routed Latvia 9-1 to win Group F. Daniel Alfredsson, the Ottawa Senators' captain, had one goal and three assists.
In Vienna, Slovakia beat Kazakhstan 3-1, and the Czechs defeated Belarus 5-1 in final Group E games.
Nash notched Canada's game-winner at 9:54 of the third on a power play, roofing a wrister from a tough angle past Ukraine goalie Kostyantyn Simchuk.
"It was fairly lucky," Nash said. "The puck rolled a bit and that helped it go top corner. But in those type of games you take them any way you can get them."
Linemate Joe Thornton, tied with Nash for the event's scoring lead with 11 points, got an assist.
Brendan Morrison gave Canada a 1-0 lead at 6:43 in the first, backhanding in a loose puck. Andrei Sryubko evened the score four minutes later with a goal between Martin Brodeur's pads.
With the championship reaching its knockout stage, the Canadians know they must play better.
"We definitely have to improve our game," Nash said. "I feel we will step up once we get the good teams. Playing games like today is tough for us.
"They [Ukraine] battle real hard, they don't give up much. Their goaltender really played well."
Jaromir Jagr led the Czechs with a goal and an assist against Belarus in Vienna's Stadthalle. The Czechs finished second in Group E behind Russia.
Petr Cajanek, Jan Hlavac, Martin Straka and Vaclav Varada also scored for the Czechs to set up a rematch of their 2004 quarterfinal against the US, who won in a shootout.
The four-time world champion Czechs dominated Belarus, outshooting them 48-10. Only outstanding Belarus goalie Sergei Shabanov kept the scoreline down. Konstantin Koltsov scored for Belarus.
"We played nearly perfect hockey tonight," Hlavac said. "The scoreline could even have been higher, but their goalie made some amazing saves."
Earlier in Vienna, Miroslav Satan put Slovakia ahead on a power play at 5:58, but Andrey Ogorodnikov pulled Kazakhstan level on its first power play four minutes later.
In the second period, Satan assisted on Ziggy Palffy's fourth goal in the tournament to give Slovakia the lead.
The Slovaks kept putting their opponents under pressure, but were not able to convert their chances until Michael Handzus netted a pass from Richard Zednik to score the game's only goal at equal strength at 2:54 in the third.
"It was tougher than we had hoped for, but we were also pretty tired," Slovakia coach Frantisek Hossa said.
Kasper Degn scored midway through the third period to give Denmark a 3-2 victory over Germany and avoid relegation.
The win gave Denmark four points atop the relegation-round standings.
Germany was next with three points, followed by Slovenia on two, and host Austria with one.
Austria meets Slovenia in the last relegation-round game on Wednesday. The two top teams will stay in the championship next year, while the last two are demoted.
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