Russia then downed Japan 2-1 and, along with Sweden, earned a spot in the tournament's quarterfinals.
Sweden was clinging to a 1-0 lead when Ostberg kicked off an offensive surge. Kim Martin Hasson made 21 saves to record the shutout.
Russia came up with a go-ahead goal from Alexandra Vafina with 8:24 to go in the third period to pull out a win against Japan. The Japanese allowed only three goals in their first two games of the tournament, but lost both.
In a unique format put in place for the women's tournament, the top four ranked teams in the world -- the United States, Canada, Finland and Switzerland -- were placed in the same group. The top two teams from that group, which will be the United States and Canada, will move on to the semifinals.
Finland and Switzerland will be joined by Russia and Sweden in the quarterfinals.
Group action must still be completed, however. Canada will take on Team USA Wednesday -- although that game turns out to be only an exhibition contest. The Canadians and Americans are expected to meet again in the gold medal game Feb. 20.
Notable deaths of 2014 [PHOTOS]