Crosby was easily the best player on the ice scoring a goal and adding two assists as Canada lived up to their billing as tournament favourites.
"I feel good," said Crosby, who won his second Stanley Cup with the NHL's Pittsburgh Penguins three months ago. "The fact I played late into June and you're stepping into this level I think that helps with adjusting."
The Canadian captain opened the scoring near the midway mark of the first period when he took the puck from behind the net and cleverly flicked it in off the back of the Czech goalie to send the two-time defending Olympic champions on their way.
Crosby then assisted on Brad Marchand's goal late in the first period and had the helper when Joe Thornton made it 4-0 early in the second.
Carey Price, back from injury and playing in his first meaningful game since last November, made 27 saves for the shutout while Patrice Bergeron, Jonathan Toews, and Alex Pietrangelo had the other Canadian goals.
The win leaves Canada tied atop the Group A standings with Team Europe following the latter's 3-0 upset win over a U.S. team that were originally considered a lock to advance beyond the group stage.
Team Europe, a roster made up of players representing eight different countries, scored on their first shot when Slovakian Marian Gaborik took a perfect feed from Denmark's Frans Nielsen and redirected it past U.S. goalie Jonathan Quick.
They added two more goals in the second when Germany's Leon Draisaitl finished off a give-and-go with Switzerland's Nino Niederreiter while Frenchman Pierre-Edouard Bellemare added another with 1:28 left in the period.
Team Europe may be the oldest and slowest squad competing in the eight-team tournament and were a popular pick to finish last before the competition began, but they quickly sent a message that they have loftier ambitions.
"We've come here to play nine periods (three games) and like everyone else we want to be playing next weekend, that was from the get-go the reason for us to be here," said Team Europe coach Ralph Krueger, who is also chairman of English Premier League side Southampton FC.
"We didn't see ourselves as just a sideshow ever."
Goaltending was expected to be the strength of the U.S. team but was shaky in the opener as Quick allowed three goals on nine shots through two periods while European counterpart Jaroslav Halak stopped all 35 shots he faced.
The stunning loss means the United States most likely need to win both of their preliminary-round games and get some help to have a chance at reaching the semi-finals.
"This is not a marathon as coaches always talk about in the NHL season, this is a sprint and we've put ourselves in a spot now where we are chasing the tournament," said U.S. coach John Tortorella, whose team resume play on Tuesday against Canada.
"It's a spot we didn't want to be in, it is a very dangerous spot but we are here."
Group A action resumes on Monday with Team Europe playing the Czech Republic.
(Official scorer's correction in para five)
(Additional reporting by Jonathan Turner; Editing by Steve Keating)
