Brodeur and Switzerland's Jonas Hiller after the game.

VANCOUVER -- Sidney Crosby and Martin Brodeur gave Canada a memorable victory and two points -- one less than the Canadians had planned on.

Crosby scored in the fourth round of the shootout and Brodeur stopped all four Swiss shooters to give Canada a 3-2 victory over underdog Switzerland on Thursday night.

Canada couldn't hold a 2-0 lead in the second period and couldn't solve Jonas Hiller in the third period and overtime despite outshooting Switzerland 47-23. Brodeur and Hiller matched saves through three rounds before Crosby -- who had been stopped in the first round -- zipped a wrister from 12 feet past Hiller's stick. Brodeur then stopped Martin Pluss, setting off an eruption at Canada Hockey Place.

The two points for the shootout victory left Canada with five through two games -- one behind the United States, which beat Norway 6-1 earlier in the day for the full three. The Canadians and Americans meet Sunday night in the game that will decide the Group A title and earn the winner a bye into the quarterfinals.

Switzerland, a 3-1 loser to the U.S. on Tuesday, got its first point of the tournament.

The hosts surprisingly found themselves in a tie game after regulation as the Swiss scored two unanswered goals in the second period, including a shocking equalizer from forward Patrick von Gunten with only 10 seconds left on the scoreboard clock.

Von Gunten got hearts racing across Canada when his shot from the left circle during a delayed penalty hit off Patrick Marleau's left skate and deflected into the net. The goal stunned the capacity crowd -- and it may have even stunned the Canadian team as they headed into the locker room.

With the game locked at 2-2 and tension building, Canada went on the power play with just 2:51 remaining in regulation as Thierry Paterlini was called for hooking Crosby as he tried to shoot.

Hiller stopped a shot from Crosby about 40 seconds into the man advantage and the Swiss cleared the puck. Hiller then stood his ground and stopped Marleau on a redirect from the high slot with 1:40 to play. It was Canada's 40th shot of the game.

The Swiss killed the penalty, leaving Canada 1-for-7 on the power play in regulation.

Off a faceoff with 30 seconds left, Hiller had to make another incredible save, this one on Nash. It was his final one of regulation.

Hiller in fact made Swiss and Canadian fans think of Martin Gerber with his performance, especially in the third period. Gerber stoned the Canadians four years ago for a 2-0 win, and Hiller was just as good, especially in the third period when he made some stunning saves to keep the Swiss in it.

None were bigger than the two he made on his Ducks' teammates, Corey Perry and Ryan Getzlaf, with about 7:30 to play in regulation. First, he stoned Perry with his stick near the left post and then he committed highway robbery on Getzlaf with a remarkable glove save.

Hiller also preserved the tie with 4:23 to play when he stoned Dany Heatley from in tight.

Switzerland did a fantastic job of matching Canada's physicality and speed. When the Swiss sensed their opportunity in the third period, they most definitely went for it and for periods of time had taken control of the game as Canada fought to match their energy.

Canada came hard early in the third period as coach Mike Babcock switched around his lines. He used both Patrice Bergeron and Jonathan Toews with Crosby and Rick Nash, taking Jarome Iginla away from that duo. He seemed to settle on Toews.

Crosby had a great chance on his backhand after a hard rush to the net, but Hiller stopped that and then also got a piece of the rebound attempt off Scott Niedermayer's stick.

Brodeur had to come up with a huge save through some traffic on a shot from Rafael Diaz from the top of the right circle at 7:46. Just a few seconds later he stopped Sandy Jeannin's attempt from close in by getting a piece of the puck with his glove.

Canada scored early in the second period on the power play as Marleau put home a loose puck from the slot just 35 seconds in to make it 2-0. The Swiss gave Canada another power play seven seconds later when Raffaele Sannitz shot the puck out of play for a delay of game.

Canada held the puck for nearly the entire two minutes but didn't shoot enough. The Canadians had another power play later in the period, but failed to get anything going and fell to 1-for-6 on the power play.

A key error by Canada's youngest player, 20-year-old defenseman Drew Doughty, led to Switzerland's first goal at 8:59.

Doughty got hemmed in the attacking zone as the puck squirted free into the neutral zone, creating a 2-on-1 for Swiss forwards Ivo Ruthemann and Martin Pluss. Ruthemann carried the puck into the left circle and instead of trying to feather a pass around Scott Niedermayer, he rifled a shot that clanged off the right post, caromed across the goal before touching the netting inside the left post.

Canada also got a scare shortly after when Shea Weber's blistering slap shot from the right point caught Heatley square in his right biceps. Heatley skated off immediately, wincing in pain and clutching his arm. However, he didn't miss a shift.

Heatley also got hit by a Weber slap shot on the play that led to Marleau's power-play goal. The shot hit both Swiss defenseman Luca Sbisa and Heatley before dropping in the slot, where Marleau found it and poked it home.

Canada grabbed a 1-0 lead going into the first intermission on a goal by Dany Heatley, his third of the tournament so far.

The puck got rimmed around the boards and Jonathan Toews won it in the corner. He fed Marleau, who found Heatley in the slot. Heatley was able to tuck it around Hiller's right pad 9:21 into the period.

Canada, which outshot the Swiss 17-8 in the first, had plenty of chances to score more, but went 0-for-3 on the power play and couldn't really establish much possession either. The Swiss cleared the zone five times during the Canadians second power play.

Brodeur looked to make a dazzling save on Rafael Diaz's slap shot off the rush with his catching love roughly midway through the period. He snared it out of the air, but the puck might have been heading high and wide.

Nevertheless, Brodeur, who stopped all eight shots he faced in the first 20 minutes, made that one look like a beauty.

-- Dan Rosen