TRoy Stitcher handed it to Mangiapane and the Flames striker finished the debate at 2:12 in the extra period.
Mangiapane left the disc to Stecher who defeated two competitors, before handing it over to his teammate.
The maple leaf will face the Americans on Saturday, while Finland will play the Germans.
Canada lost their first three matches in Riga and narrowly advanced to the playoffs. The Russians led their group with six wins in the preliminary stages.
Adam Henrik equalized the score in the power match in the third inning. The Russian top scorer was Yevgeny Timkin.
Darcy Comber saved 24 exports, one difference from Sergey Bobrovsky.
In the other quarter-finals, Germany beat Switzerland 3-2 in a penalty shootout, the United States beat Slovakia 6-1, and the Finns beat the Czechs 1-0.
In the American Clan, Colin Blackwell and Conor Garland scored twice, backed by goals from Brian Boyle and Sasha Chmelevsky.
Cal Peterson blocked 27 shots, helping his team win the seventh game in a row.
Germany reached the quarter-finals for the first time since 2010.
After trailing 2-1, the Germans withdrew their goalkeeper in the last moments of the third. Leon Gawanke took the opportunity to equalize the match with 44 seconds left. They went on to win the penalty shootout 2-1, when Marcel Noebbels defeated Leonardo Genone.
Matthias Niederberger only allowed Timo Mayer’s goal from five Swiss shooters in the penalty shootout. Dominic Kahun scored Germany’s other goal.
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