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The Americans' prospects of reaching the knockout round had looked uncertain after a loss to Canada a day earlier. But they dominated the Slovaks almost from the start and will next play the Czech Republic on Wednesday.
Cole Bardreau opened the scoring in the fourth minute before Slovakia's Matus Matis tied it 14 seconds later. The Americans built an insurmountable lead, helped by two goals apiece from Vince Trocheck and John Gaudreau.
Canada stayed in first place in Group B by downing Russia 4-1. Jonathan Huberdeau, Mark Scheifele, Dougie Hamilton and Jonathan Drouin scored for Canada. Nikita Kucherov scored in the 17th minute for Russia, which will next play Switzerland.
In Group A, the Czech Republic beat Switzerland 4-3 in overtime. Tomas Hertl scored the winner on a pass from Dmitrij Jaskin. Group leader Sweden defeated regional rival Finland 7-4, demoting Finland to the relegation round.
Group leaders Canada and Sweden draw byes in the quarterfinals.