Switzerland went unbeaten in their round-robin campaign at the Milano Cortina Games but missed out on the final after losing to world champions Britain in the semis on Thursday.
Some strategic shot-making from Switzerland in the second end helped them set up a three-pointer for Benoit Schwarz-van Berkel, before they stole another to take a 4-0 lead early on.
After a single for Norway, Schwarz-van Berkel struck again in the eighth end with a runback to add two more points to Switzerland's tally and give them a 6-1 advantage.
Norway never really threatened to get back into the contest and, after a miss from Magnus Ramsfjell opened a three-point steal for the Swiss in the eighth, the Norwegian skip conceded in some style, doing a 360 spin delivering his last throw.
It is Switzerland's eighth curling medal overall and first since they won a men's bronze at Pyeongchang 2018.
Brad Jacobs' Canada face Bruce Mouat's Britain, the world champions, in the gold medal game at the Cortina Curling Olympic Stadium on Saturday.