Crosby, playing with forwards Patrice Bergeron and Brad Marchand, had a goal and two assists, turning in the same type of dominating performance that marked his play during the 2014 Sochi Olympics.
Canada defeated Sweden for the gold medal in that tournament, when it allowed three goals and scored 16 in six games.
Video: CZE@CAN: Marchand deflects Burns' one timer
Crosby's showing for Team Canada in its Group A opener came 95 days after he won the Conn Smythe Trophy as MVP of the Stanley Cup Playoffs, when his Pittsburgh Penguins won the championship in six games.
"I feel good," Crosby said. "The fact that I played late into June and you're stepping into this level, I think that helps kind of with adjusting, and I think that finding chemistry with us as a line early has helped.
"With our team, we have so much speed and so much depth, I think that if we get things rolling, everyone kind of helps each other."
Lost among the Team Canada offense was a great comeback performance by goalie Carey Price, who made 27 saves in his first competitive game since he injured his knee Nov. 25 playing for the Montreal Canadiens.
Price was the Canada goalie in Sochi and stopped 103 of 106 shots in that tournament, earning the best goalie award. He said that Saturday felt very similar to the team he watched in front of him there.
Video: CZE@CAN: Toews chips puck over Neuvirth from the slot
"Obviously, the ice is different, so everything happens a little bit quicker," Price said of the NHL dimensions. "There's less time for our guys to hold on to the puck, but I thought our guys showed a lot of poise, made it really difficult for them to come up the ice, and that's the type of hockey that we play.
"We make it hard to get on the offensive side of us and make it really difficult to come up the ice. Our puck pursuit was relentless all night. I think that's what provided the result that we got."
After an even start, Crosby turned the game on its head with a dominating 12 minutes. He scored the first goal at 8:26, banking a shot off goalie Michal Neuvirth.
Marchand scored at 17:08, deflecting a shot from Brent Burns after Crosby won the faceoff to start the play. Bergeron scored with less than one second left in the first period, with Crosby serving as a screen, to make it 3-0.
"It's easy to play when it is a 3-0 hockey game," Team Czech Republic forward Martin Hanzal said. "After that, they were playing the game they wanted, and that was the result."
Joe Thornton scored at 7:22 of the second period by shoveling the puck into the net after a slap pass from Crosby temporarily froze the Team Czech Republic defense and Neuvirth.
Forward Jonathan Toews and defenseman Alex Pietrangelo each scored a power-play goal.
Video: CZE@CAN: Crosby opens the scoring from a sharp angle
Goal of the game:
Crosby picked up a missed shot to the right of the Team Czech Republic net and wheeled behind it, beating defenseman Jakub Nakladal to the other side and banking a shot off Neuvirth's shoulder for a 1-0 lead.
Save of the game:
Neuvirth was not as bad as the score might suggest. He made several good saves among his 44, but none better than the lunging blocker save he made on Steven Stamkos with seven minutes remaining in the second period.
PLAYER & PUCK TRACKING INSIGHTS from
In distance traveled, Team Canada defenseman Drew Doughty skated 5,296 meters (3.29 miles) Saturday.
Unsung moment of the game:
Crosby was spectacular throughout the first period, but one play went unnoticed by many. In the last minute, Roman Cervenka made a beautiful pass to spring Vladimir Sobotka alone on Price. But Crosby broke up the play with a backcheck.
Highlight of the game:
Crosby threaded a backhand pass past defenseman Andrej Sustr right onto the stick of Thornton, who only had to shovel the puck into the net for a 4-0 lead.
Video: CZE@CAN: Thornton buries Crosby's slick pass
They said it:
"I believe we were ready to play. But after the first goal, it almost seems like we stopped playing and started making bad plays, and they filled our net." -- Team Czech Republic assistant coach Vinny Prospal
"I'm not happy with six goals against, but I battled hard. After [the] first period, I told myself, 'Just enjoy it, you're playing Canada, the home team, against the best team and just to try to have fun.'" -- Team Czech Republic goalie Michal Neuvirth
"Hockey Canada, we play very good defensive hockey. We make it really difficult to score goals. Look at the roster and how many championship players are on this team, and there's a reason why they're champions. They play the game the right way, they're on the right side of the puck at the right time." -- Team Canada goalie Carey Price
Video: CZE@CAN: Pietrangelo wrist a perfect shot by Neuvirth
Need to know:
Team Czech Republic center Radek Faksa did not play in the final two periods. … Team Canada scratched right wing Claude Giroux, defenseman Jake Muzzin and goalie Braden Holtby. Team Czech Republic scratched left wing Michal Birner, defenseman Tomas Kundratek and goalie Ondrej Pavelec.
Team Canada: A two-day layoff before playing Team USA in what will be a make-or-break game for the Americans on Tuesday (8 p.m. ET; ESPN, SN, TVA Sports).
Team Czech Republic: A game against Team Europe, which defeated Team USA 3-0 Saturday, on Monday (3 p.m. ET; ESPN2, SN, TVA Sports).
Video: Recap: Price, Team Canada shut out Czech Republic 6-0