Hilary Knight, Kelli Stack and Alex Carpenter all scored to get the American bid for a gold medal off to a solid start.
Canada has won the last three Olympic gold medals awarded in women's hockey and Vetter was a member of the American team that came in second four years ago in Vancouver.
She had to make only 14 saves in the U.S. debut Saturday and did not surrender a goal until Susanna Tapani scored with 4:38 left in the third period.
By that time the Americans had built a 3-0 lead. Knight put the United States in front just 53 seconds into the game and the Americans eventually outshot Finland 43-15.
The women's tournament includes eight countries, divided into two groups. The top finishers in each group automatically make it to the semifinals while the second and third-place finishers will advance to the quarterfinals.
The United States and Finland join Canada and Switzerland in Group A. The Canadians began defense of their gold medal with a 5-0 decision over Switzerland.
Sunday's Group B games will send Sweden against Japan and Russia against Germany.