Martin Thornberg opened the scoring for Sweden one minute into the second when a pass from Tony Martensson from behind the net bounced off his leg and past Swiss goalie David Aebischer.
Defenceman Anton Stralman scored a power-play goal at 3:46, splitting the Swiss defence and putting a wrist shot past Aebischer's glove side to make it 2-0.
Patric Hornqvist added another power-play goal at 4:43 and Johan Davidsson scored twice before the second intermission.
Rickard Wallin scored seven minutes into the third to complete the rout for Bengt-Ake Gustafsson's team.
"After the first period we talked about going to the net more and creating more chances," said Wallin. "We were able to do that. They didn't stand up well in the second and that was the difference."
Sweden, with only one NHL player on its roster, will play Denmark in the qualification round on Thursday.
Swedish goaltender Johan Backlund faced only eight shots on his way to the shutout.
Switzerland finished second in Group A and will play Finland on Thursday. Italy will face host Russia on Friday in the qualification round. Germany faces the Czechs on Thursday while Latvia, Norway, Ukraine and Austria head to the relegation round.
Meanwhile, Jason Cirone scored in overtime to lift Italy to a 4-3 win over Latvia while Michael Wolf scored twice to lead Germany to a 5-3 victory over Norway.
Italy, which improved to 1-2 in the preliminary round, finished third in Group A and will face host Russia on Friday in the qualification round.
Andre Signoretti set up the winner when he skated through two Latvian defenders and fed Cirone, who took the pass off his skate and then sent the puck past the outstretched pad of Latvian goaltender Sergejs Naumovs at 4:10 of the five-minute overtime period.
"It was a pretty easy goal for me," Cirone said. "Andre did all the work taking three guys with him and all I had to do was shoot it in."
Italy looked set for the win in regulation but Lauris Darzins scored his second goal of the game, taking a pass from Mikelis Redlihs and beating Italy goalie Guenther Hell at 18:09 to tie the game at 3-3 and force overtime.
Latvia scored midway through the third to go up 2-1 on a goal by Kaspers Daugavins but Italy tied it at 16:41 when Luca Ansoldi's shot deflected off a Latvia defender and got past Naumovs.
Italy then took a 3-2 lead one minute later when Naumovs gave up a huge rebound and Christian Borgatello sent the puck in from the faceoff circle.
Italy tied the game 1-1 early in the second period when Cirone tapped in a rebound through the legs of Naumovs at 3:03.
Latvia scored the only goal in the first period. Darzins redirected a shot from the point and then picked up his own rebound before sliding the puck past Hell at 14:57.
Latvia will play in the relegation round along with Norway, Ukraine and Austria.
Germany jumped out to a 2-0 lead on power-play goals from Michael Hackert and Wolf in the opening period.
But after the break, Norway pulled ahead with three quick goals by Mats Trygg, Morten Ask and Lars Erik Spets.
Their lead was short-lived, however, as the Germans immediately responded with a scoring spree of their own. Wolf scored his second just 25 seconds later, with John Tripp adding what would be the game winner less than three minutes after that.
Alexander Barta added the insurance goal at 22:51.
"We played desperate hockey today," Germany coach Uwe Krupp said. "Both teams were very evenly matched. Tomorrow we have a very difficult opponent in the Czechs, who had the day off today. They are the strong team with more talent and more experience. But we'll fight."