Elsewhere, United States made it two wins from two Group B games by beating Switzerland 3-2.
The Canadians trailed 1-0 to the Slovaks who had also lost their first match against Czech Republic.
Karol Sloboda opened the scoring in the Group A encounter on a powerplay midway through the second period but Canada soon levelled when Jason Garrison's shot deflected off Joel Ward to beat goaltender Jan Laco.
The third period was one-way traffic as the North Americans took control.
Cody Hodgson made it 2-1 before Vancouver Canucks defenseman Kevin Bieska drove a slap shot beyond Donbass Donetsk netminder Laco.
Canada added a fourth goal when Ward netted following a good pass from Alex Burrows.
The U.S. crushed hosts Belarus 6-1 in their opening game but the Swiss proved much tougher opposition even though they had been thrashed 5-0 by Russia a day earlier.
Denis Hollenstein put the Swiss ahead early in the second period before Peter Mueller struck for the Americans.
The U.S. trailed again when Damien Brunner scored but Craig Smith of the Nashville Predators levelled early in the third period on the powerplay.
With less than seven minutes remaining the Tampa Bay Lightning's Tyler Johnson grabbed the winning goal.