Sweden crushed France 4-0 in Group F while Czech Republic, the holders, defeated hosts Slovakia 3-2 in Group E.
Mike Komisarek of the Toronto Maple Leafs put the U.S. ahead in their Group F qualifying-round game before Brent Burns leveled for Canada.
Jack Johnson gave the Americans a 2-1 advantage but John Tavares and Jason Spezza replied in the third period. Derek Stepan then squeezed a shot past netminder James Reimer to set up overtime.
Rick Nash and Jordan Eberle scored in the shootout while Reimer saved from Johnson and Blake Wheeler.
"We pushed the pace and that is exactly what we wanted to do," Canada coach Ken Hitchcock told reporters.
"These are tough games to play for goalies and today Reimer played well. I was happy for him that he did so well in overtime."
Canada lead Group F with seven points. They face Norway on Saturday while the Americans take on France.
The Czechs narrowly beat Slovakia in a meeting of the two countries that formed a joint state until 1993.
Minnesota Wild defenseman Marek Zidlicky opened the scoring after redirecting Patrick Elias's slapshot in the first period before Ladislav Nagy leveled for Slovakia.
Martin Havlat and Patrik Elias put the Czechs 3-1 up before Tomas Surovy pulled one back for the home team with two minutes to go.
In Group E, Carolina Hurricanes left wing Tuomo Ruutu put Finland in front before Germany replied through Andre Rankel after 14 minutes.
Germany, who shocked Russia and Slovakia in the preliminary round, rallied to take a 3-1 lead thanks to Felix Schutz and Kai Hospelt before Janne Pesonen and Jarkko Immonen leveled the scores.
Patrick Reimer struck late in the second period to give Germany a 4-3 advantage before Ruutu scored his second late in the third to take the game into a scoreless overtime.
Mikko Koivu then struck in the shootout to seal the win for Finland.
(Additional reporting by Petra Kovacova in Bratislava, editing by Tony Jimenez)
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