Both teams struggled to find their scoring touch early on, but Canada recovered more quickly, opening a three-goal lead in the second period on their way to an easy win. Rebecca Johnston and Melodie Daoust each scored two.
The U.S. had to come from behind after Finland struck first with a goal in the final six seconds of the first period from forward Venla Hovi.
Second-period goals by Kendall Coyne and Monique Lamoureux-Morando put the U.S. on top. Their two-goal margin of victory came courtesy of a late empty netter by Dani Cameranesi with Finnish goaltender Noora Raty pulled for an extra attacker.
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Sunday's result - on the scoreboard at least - was a stark contrast to the typical opening Olympic clash for the two teams.
In the previous five openers, the U.S. had outscored their opponents by a combined 36-2 and Canada had amassed 59 goals and given up none, although the outcomes began narrowing in Sochi when the preliminary round structure was revamped to place the top teams in the same group.
"I think it is a testament to the parity within our sport and how close it's getting," Canada head coach Laura Schuler said. "You're really seeing that at the U-18 level and how close it is. It's a positive thing."
The U.S. came into the game with a scoring problem. In their last four pre-Olympic international friendlies, all against arch-rival Canada, the Americans were outscored 9-3. The two face each other again in the final round-robin game on Thursday.
Like Canada in their game against the Olympic Athletes from Russia, the U.S. dominated time of possession and put plenty of pucks on the net - out-shooting Finland by a 42-24 margin - but struggled to capitalise.
"We believe this tournament is going to be very hard fought and it was tonight," U.S. head coach Robb Stauber said.
"It's an absolute great way to start because you want it to be tough. It is a great indication of what it is going to take to win the Olympics."
(Additional reporting by Steve Keating; Editing by Toby Davis)
