Goalkeeper Martin Gerber displayed nerves of steel in front of the Swiss net and Reto Suri converted twice in the shootout for Switzerland.
The Swiss had already beaten co-hosts Sweden in their opening game.
In Helsinki, Ilya Kovalchuk's hat-trick helped Russia to a comfortable 4-1 victory over Germany as the defending champions maintained their grip on top spot in their group.
The United States came back from a goal down to beat Latvia 4-1, twice punishing the Latvians with powerplay goals, and Damien Fleury netted his second goal of the tournament as France beat Austria 3-1 in other games in the Finnish capital.
In Stockholm, Belarus registered their first win of the tournament as they edged out Slovenia 4-3 thanks to a late goal from forward Alexei Ugarov.
Norway wasted no time in taking the upper hand against Nordic neighbours Denmark as Mats Trygg scored in the second minute to put his team ahead.
The Danes fought back to 2-2 in the third period, but a Patrick Thoresen goal with 2:32 left on the clock sealed the victory for Norway.
- Sports & Recreation
- Ilya Kovalchuk