Schwarzer was helpless with both goals, the first from Adriano early in the second half and the second from Fred in the dying minutes of the game.
Viduka was well shackled by the Brazilian defence but was unkucky to see his best effort loop over the bar after he beat the keeper to a loose ball.
2-0 probably flettered the South Americans who were not at their best and Australia will be disappointed not to get something out of the game. They had several good chance in the second half but failed to hit the target.
The Socceroos need a least a draw against Croatia on Thursday to reach the knock-out stage.