Striker Josh Kennedy had time to turn and strike the ball home from close range in the 71st minute to seal a morale boosting over a well organised Danish side.
Australia, the first side to arrive in South Africa for the June 11 to July 11 World Cup, spent much of the match at Roodepoort's Ruimsig Stadium on the back foot but stout defending rarely allowed Denmark any clear cut chances.
"We did well defensively, playing a very compact game but we struggled when we had the ball. We still need time to adjust to the altitude," Australia coach Pim Verbeek told reporters.
Denmark coach Morten Olsen said the match had provided much needed preparation.
"We had a lot of the ball but it doesn't matter in football how much possession you have, it is scoring goals that counts," he said.
Both teams play again on Saturday in final warm-up games. Australia take on the U.S. at Ruimsig while Denmark meet hosts South Africa in Pretoria.
Australia will face Germany, Serbia and Ghana in Group D, while the Danes take on the Netherlands, Japan and Cameroon in Group E.
