Jakob Silfverberg, Marcus Krüger and Loui Eriksson all scored one apiece for Sweden, while Mads Hansen was on target for Norway.
Silfverberg opened the scoring in the 17th minute after being fed by Norris Trophy candidate Erik Karlsson, beating Norway's keeper Lars Haugen with a quick shot on his near side.
Norway evened up the scores 20 seconds into the second period when Mads Hansen powered home a drive.
The Swedes were quickly out in front again however after Marcus Krüger capitalised on a cross-crease feed from Niklas Hjälmarsson to smashed it past the hapless Haugen.
Zetterberg completed the rout in with the clock at 4:18 while the Swedes enjoying a man advantage.
Norway were however gracious in defeat.
"They are kind of our big brother and you want to beat them, but they are good. Hopefully next time we can beat them," Norway's Mathis Olimb said after the match.
Holders and co-hosts Finland meanwhile got their title defence off to a winning start on Friday, beating Belarus 1-0 in their preliminary round match in Helsinki.
Spurred on by a capacity 13,000 home crowd, Finland pinned Belarus back from the opening face-off but the guests keeper Vitali Koval performed courageously stopping and deflecting all pucks thrown at him.
But Koval was unable to stop Finland's blueliner Janne Niskala breaking through with just 42 seconds remaining before the first interval.
In the second period the Finns continued peppering Koval with shots but to no avail as they lacked precision in front of the Belarus net.
"We knew that it would be a tough game," Finland manager Jukka Jalonen said. "Belarus were defending very well and it was really difficult for us to score."
Also in the Helsinki group, Vancouver Olympic champions Canada came away 3-2 winners against 2002 world champions Slovakia.
Canada, who won their last world crown in 2007, grabbed the lead through Dallas Stars forward Jamie Benn, who beat Slovakia's goalie Peter Hamerlik from close range on Ryan Getzlaf's feeding pass 14:21 into the match.
Tomas Tatar pulled the scores level 1:58 into the second period, wristing the puck into the net from the left face-off circle, but Jordan Eberle of Edmonton Oilers restored Canada's lead with a sharp-angled shot 10 minutes later.
Winnipeg Jets' striker Andrew Ladd made it 3-1 for Canada 35:21 into the match, when he redirected Ryan O'Reilly's cross into the net.
Milan Bartovic reduced the arrears 2:59 into the third period but failed to save the day as Canada defended stoutly and kept their advantage through.
"It was a tough match as Slovakia are traditionally strong opponents," Canada skipper Ryan Getzlaf said.
"I remember that the previous matches with them were also pretty tough."
"We still need time to adjust our playing to the European ice rinks' size, but we all want to keep getting better. We know it's going to be tougher from one match to another. And our next match with USA will show whether we're ready for it."
The world hockey championships continues in Stockholm and Helsinki until the final on May 20th.