It was the second no-hitter in as many days for the Americans, who are overwhelmingly favored to win the softball gold medal for the fourth time in as many tries.
The International Olympic Committee has voted to remove softball from the Olympic program for the 2012 Games but officials of the sport have petitioned to have it reinstated.
Jennie Finch didn't allow Venezuela a hit Tuesday in the United States' opening game but that 11-0 victory was shortened to five innings by the 10-run rule.
Osterman's performance came over the full seven innings against the team that was expected to give the Americans their toughest test in the Olympics. Australia has won two bronze medals and one silver in the sport.
The game was scoreless into the fifth inning but Natasha Watley singled in a run in that frame and Crystl Bustos added a 2-run home run in the sixth.
Osterman threw only the second seven-inning no-hitter in Olympic history. The United States' Lori Harrigan produced a perfect game against Canada in 2000. Osterman walked three batters Wednesday.