Germany sprung an upset on the first day of the 16-team tournament by beating Russia 2-0, with Slovakia and Switzerland also winning. The U.S. begins Saturday, facing Austria in Kosice.
Eberle put Canada ahead with a backhand 1:52 into the opening period, and Andrei Stepanov tied it with 34 seconds left in the period after a defensive blunder by Luke Schenn.
Jeff Skinner restored Canada's lead, beating goalie Andrei Mezin with a wrist shot in the second period off an assist from John Tavares. Skinner then set up Tavares to make it 3-1 before Eberle completed the scoring by tapping in a rebound off the post.
"It's a good start," Eberle said. "We played pretty well and as the game went on we got better."
Added Canada coach Ken Hitchcock: "Belarus played with a lot of desire. They gave us a real good test."
In Bratislava, Germany topped Russia on goals by Thomas Greilinger and Patrick Reimer, and Slovakia defeated Slovenia 3-1.
In Kosice, Switzerland beat France 1-0 in overtime on a goal from Julien Vauclair. The game was interrupted for nine minutes in the third period because of a power blackout at Steel Arena.
Germany earned its first victory over Russia at the worlds. Goalie Dennis Endras had 31 saves to help the Germans avenge a 2-1 loss to Russia at the semis of last year's worlds, which they hosted.
"We made history," forward Andre Rankel said. "This gives us a lot of confidence for the tournament."
Russia, the most successful team in worlds history with 25 trophies, mounted pressure toward the end of the game, outshooting Germany 12-5 in the final period. But Ilya Kovalchuk, Alexander Radulov and Vladimir Tarasenko failed to convert.
"They played much better than us," Russian coach Vyacheslav Bykov said. "We had our chances but couldn't score."
The underdog French won when Vauclair took the puck from Ivo Ruthemann and scored on a solo effort 1:46 into sudden death.
"I like those kinds of plays," Vauclair said. "I just took my chance, ran over and scored."
Swiss goaltender Tobias Stephan stopped 29 shots.
"Sometimes we don't shoot enough when we have chances," French coach Dave Henderson said.