The Americans (4-0) got everything and more from the upstart Swiss, who hoped to advance despite being the lowest-ranked team left in the tournament. Parise sealed the win with his second goal, an empty-netter with 11.2 seconds remaining.
Swiss goalie Jonas Hiller of the Anaheim Ducks kept it a contest by making 42 saves. Switzerland recorded 19 shots on Ryan Miller.
The Americans will face the winner of Wednesday's game between the Czech Republic and Finland on Friday, with a place in the gold medal game on the line.