Parise produced a power-play goal 2:08 into the final frame to finally crack the wall that had been formed by the Swiss defense and goaltender Jonas Hiller.
The Americans did not clinch the game, however, until Parise won a battle at the blue line and then put the puck into an empty net with 12 seconds to play.
Team USA, which won only one game in the 2006 Olympics, improved to 4-0 in Vancouver and will meet either Finland or the Czech Republic on Friday with a spot in the championship contest on the line.
Ryan Miller of the Buffalo Sabres, who has been in goal for every minute of U.S. action at these Olympics, made 19 saves for the shutout.
The American team, meanwhile, put 44 shots on goal against Hiller of the Anaheim Ducks.
Although Hiller was brilliant as part of a defense-first philosophy for the Swiss, the United States was unfortunate not to have scored at least two other goals.
An apparent score at the end of the second period was negated when it was ruled the puck crossed the goal line after the horn had sounded.
In the third period, another potential goal was wiped out because of a penalty called on Ryan Kesler before the shot
The United States men's team is looking for its first hockey gold medal since the 1980 Olympics, when the Americans stunned the powerful Soviet Union team in the medal round.
Copyright 2010 United Press International
USA is playing great
I am cheering for Canada, but the US is playing great. I think Patrick Kane is awesome, along with praise and bobby ryan. If Canada meets US in the finals it will be a very good game. Miller stood on his head during the last game, but I think the Canadian team has improved a lot since that game.
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