Klose, leading scorer in the 2006 World Cup, managed to get 2- in the 27th minute with a well-taken goal - and his 11th in World Cup finals - rising among Australian captain Lucas Neill and Schwarzer to head strongly home from a Lahm cross.
"Every thing worked properly in fact it is critical that things gone properly during the 1st game," Klose explained.
"We have earned some respect. You could see that we had fun playing football out there. I know what i can do. I feel great."
Germany coach Joachim Loew was delighted too.
"I am very happy about the performance, we showed some quick passing and good speed," he said.
The Socceroos paid a heavy price for the dismissal of Tim Cahill, shown a straight red card in the 56th minute by Mexican referee Marco Rodriguez for a very clumsy challenge on Bastian Schweinsteiger.
Two goals in a matter of minutes from Mueller (67) and Cacau (70), on as a replacement for Klose, sealed Australia's dismal start to their third World Cup campaign.
Mueller, who started the season in Bayern Munich's reserves, looked like he'd overrun a Podolski through-ball it but he dragged it back and shot accurately past Schwarzer, in off the post.
With the Australian defence in disarray, Caucau then had a simple tuck-in from another inch-perfect pass into the box by the 21-year-old Oezil.
It was Australia who had the first real chance of the game, Lahm clearing a close-range effort by Richard Garcia in the fourth minute.
And for all their fine attacking instincts, Germany did at times look slow to close down at the back, allowing time and space for both Garcia and replacement Brett Holman to have shots on target.
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