Lukas Podolski and Miroslav Klose scored in the first 30 minutes as Australia coach Pim Verbeek's defensive tactics backfired. And Thomas Mueller and Cacau scored against an overwhelmed Australian defense in the second half after Cahill was red-carded in the 56th minute for a late challenge on Bastian Schweinsteiger.
The dominant win, played in front of 62,660 fans at the Moses Mabhida Stadium, came without injured captain Michael Ballack.
Germany has not lost an opening match in the World Cup since a 2-1 defeat in 1982 against Algeria and the team never looked like losing on a warm evening in Durban.
Podolski started the rout by rounding off a slick passing move in the eighth minute and Klose headed in his 11th career World Cup finals goal in the 26th.
Verbeek sat on the bench shaking his head while Joachim Loew, in his 50th game as Germany coach, punched the air.
Hoping to hold out for a draw, Verbeek used Cahill as a forward and packed his midfield. But with Cahill isolated up front instead of controlling the midfield, Australia had no answer to Germany's swift passing and running game.
Any slim hope Australia had of coming back evaporated with Cahill's sending off.
Klose missed two more good chances before Mueller made it 3-0 in the 68th, dragging the ball back to avoid a lunge from Chipperfield and sending a low shot in off the post.
Cacau rounded off the scoring in the 70th, just two minutes after coming on as a substitute for Klose.