Sinclair's goal was the 148th of her 205-game international career. The 30-year-old striker has now scored at least one international goal in 15 consecutive years.
One of the best games we've played in a while," Sinclair said. "Our focus heading into this game was to create some quality final acts and create some scoring chances and I think we completely dominated in that aspect. Scoring three goals is always nice and it was a perfect way to start the tournament."
Schmidt scored in the 32nd and 42nd minute with Sinclair increasing the lead in the 60th minute. For Schmidt, the goals were the 10th and 11th of her international career.
"Everything clicked," Schmidt said. "The movement we've been practising was working, the easy balls, the right side of the body and then just the composure to keep it, shield people off and take people on. Everything that we've been talking about came together in 90 minutes. It was beautiful and fun to play."
It marked the 65th consecutive game for Schmidt, who has played 115 games for Canada.
Rhian Wilkinson set up the second and third goals with crosses. Diana Matheson had an assist on the first.
"They were just world class," Canadian coach John Herdmann said of Schmidt's goals. "We have been asking Sophie and the midfielders to start chipping in with goals. We really didn't blow teams away in terms of the goals because we were either trigger-shy or players weren't getting into the right areas early enough. So we've been working on that. . .
"What I've got to be happy about is the movement of the players. The movement was phenomenal. The discipline behind the movement off the ball was great to see. We'll enjoy watching the highlights reel tonight."
Veteran goalie Karina LeBlanc got the shutout in her 100th start — and 108th appearance — for Canada.
Rachel Quon, 22, made her Canada debut, coming in off the bench in the 79th minute.
The win improved Herdman's record to 26-15-8 as Canadian coach. That moved the Newcastle native past Carolina Morace into second place for Canadian women's coaching wins. Even Pellerud tops the list with 66.
Canada, currently ranked seventh in the world, beat the No. 23 Finns 2-1 at last year's tournament. Finland, currently second to France in their UEFA qualifying group for the 2015 World Cup in Canada, came into the game having won its last five outings.
"That was a pretty solid performance against a good Finnish team," Herdman said. "This team very rarely gets beaten by that sort of scoreline. I'm really proud of the girls today. We've started exactly how you want to start a tournament with three goals, three points and we've got the Italians next which will be another step up."
Canada plays No. 12 Italy on Friday before concluding preliminary-round play Monday against No. 11 England.
The Canadian women are without injured defender Lauren Sesselmann (knee).
Canada has won the Cyprus tournament three times but has lost in the final the last two years: 1-0 to England last year and 2-0 to France in 2012.