Europe got a power-play opportunity of their own at 18:10 of the final regulation frame. Roman Josi rang a shot off the post behind Price to nearly take back the lead. Price then covered up a shot from the slot to freeze the puck moments later.
Then Canada came back the other way.
With 43.1 seconds left in the game, Marchand lifted Canada to their first lead of the night, shorthanded, with a snipe from the high slot.
"Just crazy the way everything worked out," said Crosby. "I mean, when you get a penalty that late in the game, you're just trying to force overtime, and then Marchy comes down and buries one like that, pretty unbelievable feeling, considering how hard we had to work to get our chances here tonight. It wasn't easy."
Canada held on in the final seconds to win the World Cup of Hockey, going undefeated in tournament play and sweeping Europe in two games.
Crosby earned MVP honours with three goals and seven assists in six games for Canada.