Canada started the scoring at 6:09 of the first period with Barrie assisting on Ryan O'Reilly's game-opening goal, and Mike Matheson found the back of the cage 55 seconds into the second period to give the World's No. 1-ranked team a 2-0 advantage.
The Czechs cut their deficit in half at 12:41 of the third frame, but Barrie scored on a one-time snap shot from the circle 2:09 later to extend Canada's lead back to two. Jeff Skinner tallied an empty-netter with 42 seconds left to seal the victory.
Barrie was on the second defensive pairing with Calvin de Haan of the New York Islanders and played 16:07.
Canada's second forward group was two-thirds Avs, with Matt Duchene and Nathan MacKinnon playing alongside team captain Claude Giroux of the Philadelphia Flyers. Duchene had one shot and a plus-1 rating in 16:43 of ice time, while MacKinnon played 13:33 and also finished with one shot and a plus-1 rating.
Pickard is at his second World Championship after helping his home country to the gold medal at last year's tournament and came up big early on while his teammates were finding their stride.
"Pickard definitely kept us in there, but it's our first game," said Canada and Winnipeg Jets forward Mark Scheifele. "We've got to build off this. Obviously we're not happy with the full game, but we had hints of brightness. So, we've just got to continue to press and get better. That's how you win in this tournament."
The two-time defending champion Canadians now get ready to face Slovenia on Sunday.
Above photo courtesy of @HockeyCanada