It was the first gold medal game in tournament history that did not feature the United States and Canada. Finland upset Canada 4-2 in the semifinals on Saturday.
Amanda Kessel and Annie Pankowski scored in the shootout for the United States, and Alex Rigsby made 26 saves, including stopping four of five attempts in the shootout.
"I'm extremely proud of our team tonight for playing their game while emotions were running high, in a loud building and against a team that played us incredibly hard," United States coach Bob Corkum said after his team won the gold medal for the eighth time in the past nine years. "It's been an honor to coach this team."
Minnamari Tuominen scored in the shootout, and Noora Raty made 50 saves for Finland.
The United States took a 1-0 lead at 15:46 of the second period when Kendall Coyne Schofield won a puck battle and fed Pankowski, who beat Raty through a screen.
Susanna Tapani tied it 1-1 at 18:29, taking a cross-ice pass from Petra Nieminen and beating Rigsby high to the blocker side with a shot from the left circle.
Nieminen appeared to have won the game on a rebound at 11:33 overtime, but the goal was overturned after a video review because of goalie interference. However, Finland was awarded a power play after tripping was called on Rigsby, and had another man-advantage at the end of overtime, but wasn't able to convert on either.
Canada won the bronze medal with a 7-0 win against Russia.
