The US had more trouble in their game later on Saturday when they rallied for a 2-2 draw with Russia.
But Finland were delighted to put their nightmare start to the tournament behind them with victory over qualifiers Belarus.
NHL stars Teemu Selanne and Olli Jokinen each scored a pair of goals as Belarus were put to the sword.
"Although the US played really well against us, we couldn't get anything going in that game," said Finland defenseman Jyrki Lumme.
"We were dumping the puck all night long. This time we played more of a European type of system of controlling the puck.
"We were able to score three in the first period which was a big help," he added.
The Finns, who dominated throughout, blasting 39 shots at Belarus goalie Andrei Mezin, then banged home two more to finish the scoring.
Florida Panthers forward Jokinen opened the scoring just 90 seconds into the game before San Jose Sharks All-Star Teemu Selanne notched his first of the tournament on a power play.
Jokinen made it 3-0 and Selanne then added his second to keep pace with his team-mate.
Carolina Hurricanes forward Sami Kapanen and Atlanta Thrasher Tomi Kallio also scored before the end of the second period.
Vasily Pankov broke Passi Nurminen's shutout bid with a power play marker four minutes into the final frame.
But Lumme's NHL team-mate Aki Berg and Los Angeles Kings forward Mikko Eloranta both found the back of the net late in the game.
In the group's other match, Brett Hull scored the tying goal with 4:30 remaining to allow the United States draw 2-2 with Russia.
Playing a masterful possession game and a hard-hitting defense, Russia kept the US team to only four shots on goal in the second period and to only one for the first seven minutes of the third period after Russia had taken a 2-1 lead.
But the Americans continued to push forward and found the equalizer through Brett Hull.
Both teams now sit atop of Group D with one win and one draw in the round-robin series that will determine seeds for Wednesday's quarter-finals.