The Slovaks, who suffered defeats in their first two games, scored three goals in the first period and hung on despite a desperate fightback from the US in Helsinki.
Miroslav Satan rounded off the scoring when he fired into an empty net with 39 seconds left.
Group H rivals Canada opened with a four-goal salvo in the first period as they swept aside the challenge of France .
Ryan Nugent-Hopkins and Jamie Benn each netted twice and Patrick Sharp of the Chicago Blackhawks had a goal and four assists.
In the day's games in Stockholm, the Czech Republic narrowly defeated Norway 4-3 on penalties after a 3-3 draw.
The Norwegians led 1-0 and 2-1 but could not hold on to their lead and they eventually needed an equaliser from Jonas Holøs to force overtime.
Neither side could break the deadlock in the extra period, leaving Ales Hemsky to score the winning penalty in the shootout for the Czechs.
Co-hosts Sweden were coasting and held a 6-1 lead at the halfway point in their game against Denmark , but they had to withstand a late charge from the Danes to hang on for a 6-4 victory and preserve their unbeaten record in the competition.