The big defenceman had his first attempt blocked before beating Leonardo Genoni high to seal the victory.
The Canadians looked poised to win in regulation after Chris Stewart scored while falling to the ice at 16:46 of the third period to make it 3-2. But Andres Ambuhl responded less than two minutes later, lifting a shot over James Reimer from the slot to bring Steel Arena to life.
Genoni was tremendous in the Swiss goal -- stopping 22 shots in the second period alone -- to help keep things tight.
Jordan Eberle and John Tavares
also scored for Canada.
Rafael Diaz and Felicien Du Bois had the other goals for Switzerland, a team comprised of 22 domestic league players and Anaheim Ducks defenceman Luca Sbisa.
The Swiss have been a bit of a nemesis for Canadian teams in recent years and it appeared as though that might continue through the first 20 minutes.
Diaz opened the scoring with a shot from a tough angle that fooled Reimer at 12:29 and Genoni showed the form that helped him lead HC Davos to the Swiss League title two weeks ago. The goaltender stopped all 14 shots he faced in the period.
But the Canadians poured on the pressure in the middle frame, grabbing back the lead after a scary moment where Swiss forward Simon Moser appeared to pass out on the team's bench after taking an open ice hit from Dion Phaneuf midway through. The 22-year-old left under his own power and returned for the third period.
Eberle tied the game 1-1 at 11:57 with a shot that went between teammate Matt Duchene's legs and through Genoni's five-hole. The goal came after Canada had the Swiss hemmed in their own zone for more than a minute.
The Canadians continued to pressure and went ahead 2-1 on a goal credited to Tavares at 16:51. He was carrying the puck into the slot when Swiss forward Morris Trachsler accidentally fired it into his own goal.
Matthias Bieber had a chance to tie the game early in the third period on a penalty shot, but Reimer got his blocker on the attempt. It was the third penalty shot in as many Canadian games at the tournament.
However, Du Bois soon got the equalizer at 8:38 with a wrist shot from the point through traffic that found the top of the net to make it 2-2.Notes:
Canada's Travis Zajac entered the game with the tournament's best faceoff winning percentage. ... Andy Murray, who coached Canada to gold at the 2007 world championship, is an adviser for the Swiss team. ... Canadian assistant GMs Bob Murray and Rob Blake took in their first game after arriving in Slovakia.