Having previously beaten the Czech Republic 4-2, it looked like the Swedes would have to settle for a draw as the third period edged towards it's conclusion.
But Alfredsson got the vital breakthrough on 52 minutes to break the dogged Swiss resistance and ensure Sweden stay top of Group C.
The Czech Republic moved up to second behind Sweden after getting their campaign back on track with a 4-2 win over winless Latvia.
Martin Erat got the first goal and while the Latvians pulled a goal back through Janis Sprukts, further efforts from Jaromir Jagr, Herberts Vasiljevs and Jakub Voracek secured the points.
While in Group B reigning champions Canada made it two wins from two as they defeated Austria 6-0 with Jeff Carter netting a hat-trick in the second period.
But it was not enough to put them top of the table with 2010 bronze medallist Finland storming to a 6-1 win over Norway to hold the edge on goal difference.
� Sportsbeat 2014
- Sports & Recreation
- Czech Republic