In Helsinki, co-hosts Finland also qualified for the last eight after hammering Austria 7-2 with Petri Kontiola grabbing a goal and two assists for the home side.
Tournament surprise package Switzerland are unbeaten and already boast the scalps of co-hosts Sweden and champions Russia among their victories.
Luca Cunti, Ryan Gardner and Nino Niederreiter netted powerplay goals as the Swiss punished Danish indiscipline.
Nicklas Jensen pulled the score back to 2-1 in the middle of the second period but that was as close as the Danes came in Stockholm.
United States strolled to a 4-2 victory over France, pounding 36 shots on goal compared to 17 for their opponents.
Stephen Gionta, Bobby Butler, Paul Stastny and David Moss were on target for the Americans.
Germany claimed their second straight victory as they defeated Latvia 2-0 in Helsinki to go fifth in Group H and leave the losers rooted to the bottom.
In Stockholm, Sweden managed just two goals from 40 shots but they were enough to beat Slovenia 2-0.
Norway finally netted a powerplay goal as they defeated Belarus 3-1.
The Norwegians went into the game as the only team not to have scored with an opponent in the sinbin but Anders Bastiansen broke their duck with one second remaining of Pavel Chernaok's penalty.
Per-Age Skroder hit two goals for Norway.
With the top four from each eight-team group going through to the quarter-finals, Finland lead Group H on 14 points. The U.S. are second on 12 followed by Russia (nine) and Slovakia (seven).
Switzerland top the other group on 14 points. Canada are second on 13 points ahead of Sweden (12) and Norway (9).
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