It was a better start by defending champions, The Czech Republic, who crushed Germany 8-2 on Friday.
The United States also got off to a flying start outplaying Finland 6-0 while Russia edged Belarus 6-4.
But it was Mario Lemieux's Canada team who suffered the most unpleasant opener, having come to the Games as the overwhelming favourites for gold.
Niklas Sundstrom, Kenny Jonsson and Ulf Dahlen added one each for Sweden to make that task look far from easy.
Rob Blake and Eric Brewer scored for Canada.
"Now that we know what
we are up against we will have to readjust"
The Swedes used their innovative "torpedo" system to perfection against an out-of-sync Canada side.
Sundin beat Toronto team-mate Curtis Joseph twice to lead his team to a surprisingly easy victory.
"We worked the torpedo, and it worked pretty good," said Niklas Sundstrom, who scored a goal and set up two others.
"We're used to playing on the big ice."
The result is not fatal to the medal hopes of a Canada team assembled by legend Wayne Gretzky.
But it is a warning that their quest for a first Olympic gold in 50 years will be far from straightforward.
"Obviously it was a tough loss, especially the way it all happened. We have two more games, and now that we know what we are up against we will have to readjust," said Lemieux.
In the other Group C game, the Czech Republic kicked off the defense of their 1998 title with an impressive 8-2 win against Germany.
Jaromir Jagr had two goals and two assists and Hasek stopped 18 shots as the Czechs' superstar nucleus rekindled memories of Nagano.
Robert Lang had a goal and two assists, while Martin Havlat, Petr Sykora, Milan Hejduk, Patrik Elias and Robert Reichel also scored.
Leonard Soccio and Stefan Ustorf got on the scoresheet for the German qualifiers.
In Group D, Russia withstood a feisty performance from Belarus to win their opening tie 6-4.
Although Belarus have been pegged as the weakest team in Group D, Russia, whose squad contains 21 NHL players, found their opponents to be no pushovers on Friday.
After bolting to a 4-1 lead, a second period lapse of concentration proved costly for Russia and Belarus clawed its way back to 4-3 with two easy goals.
The Nagano silver medallists regrouped in the third period with goals by Boris Mironov and Sergei Fedorov in the first four minutes to regain their three-goal lead.
Anaheim Might Ducks defenseman Ruslan Salei got one back for the qualifiers in the last two minutes of the game but it was too late to snatch victory from Russia.
In the other Group D match, John LeClair found the back of the net three times in the United States' 6-0 win over Finland.
The Americans had trouble getting past the Finns' defence in the first period, but strikes by Scott Young (9:45), LeClair (16:16) and Keith Tkachuk (17:45) put the United States in the driving seat.
LeClair (6:04 and 11:23 of the third) and Bill Guerin (14:14) completed the rout and America's first Olympic shutout since beating Poland 3-0 in 1992.
All teams in the final round take part in round-robin play for the first four days, which will decide the seedings for the quarter-finals starting on Wednesday.
In the only women's action of the day, Russia beat Kazakhstan 4-1 in a "dead" match.
Both teams had lost all their games in Group A and were already eliminated.