It is the eighth silver medal for the United States in Olympic hockey.
In the extra session, the Canadians were cycling around the left boards. Crosby pushed the puck down to the low left boards for Jarome Iginla, who fed the puck back to Crosby as he was being checked to the ice, and Crosby threw a quick shot on net that got past Ryan Miller for the win.
Jonathan Toews and Corey Perry scored a goal each in regulation for Canada, which took home its eight gold medal in hockey and first since the 2002 Games.
Roberto Luongo, who took over as the starting goaltender after Martin Brodeur was lit up by the Americans last Sunday, stopped 34 shots for Canada, which won a Winter Olympic-record 14 gold medals in these games.
Zach Parise and Ryan Kesler each had a goal for the Americans, who were looking for their first gold medal since the 1980 "Miracle on Ice" team.
Miller stopped 36 shots for the United States, which was on the losing end of the 5-2 final in 2002 against Canada.
It is the eighth silver medal for the United States in Olympic hockey. Six of those silver medals have come behind gold-medal victories by the Canadians with the other two coming as runner-up to the now-defunct Soviet Union.
Holding a one-goal lead, the Canadians put the pressure on the Americans over the first several minutes of the third period, but were unable to take a two-goal lead due to hitting the post twice.
Miller kept his team within one goal with a spectacular right pad save on Dany Heatley's rebound chance from the left side with about 10 1/2 minutes to play.
Brian Rafalski had a chance to tie the game as he wristed a loose puck from the right circle, but Luongo was there to make the save and cover up the disc with 5:05 to play.
Crosby was sprung on a breakaway with about 3 1/2 minutes to play, but Kane raced down the ice and cut off the deke to keep it a one-goal game.
The Americans got Miller out of net in the final two minutes of play and the move paid off. After several shots on net, Patrick Kane threw a shot that hit off the skate of Jamie Langenbrunner. The puck went to Luongo and Parise was there to jam home the rebound with 24.4 seconds left on the clock to tie the game.
The United States had a good forecheck going early in the game, but saw several of its shots blocked and no real solid opportunities.
With 7:10 to play in the first, Canada took the lead. A turnover deep in the American zone saw the puck come to the low right circle where Mike Richards threw a turnaround shot on net. Miller made the stop, but the rebound kicked out to the right side where Toews wristed it home.
Luongo made eight saves in the opening period to keep the Americans off the board.
After each squad had a power play opportunity early in the second period, the Canadians took a 2-0 lead.
Ryan Getzlaf skated down the left side and from the circle threw a backhand pass to the slot. Patrick Marleau was charging hard to the net and the puck deflected off the stick of Ryan Whitney. From there, it trickled back to Perry, who wristed the puck past Miller.
Toews was called for tripping shortly after the goal to give the United States its second power play of the game, but the Canadians kept the opportunities away from Luongo.
The Americans, though, did get one by Luongo with 7:16 to play in the frame. Kesler charged into the Canadian end through the middle of the ice and sent the puck over to Kane. From the right point, Kane threw a shot on net that a charging Kesler tipped past Luongo.
The United States nearly tied the game with about 3 1/2 minutes to play in the second, but Ryan Suter's rebound chance in front of the net off a Dustin Brown shot trickled inches wide of the far post.
