(CNN) -- Germany laid down their World Cup title credentials with a ruthless 4-0 thrashing of 10-man Australia in Durban on Sunday.
Australian attacker Tim Cahill was sent off for a dangerous tackle early in the second period when the score was 2-0.
The result put Joachim Low's injury-hit team top of Group D on goal difference from Ghana, who earlier beat Serbia 1-0.
A late penalty by Asamoah Gyan gave Ghana a deserved victory in the opening Group D match played in Pretoria.
Germany 4-0 Australia
Forwards Lukas Podolski, Miroslav Klose, Thomas Muller and Cacau all scored for the three-time champions in the most one-sided match of the tournament so far.
"Everything worked well and it is important that things went well in the first game," Klose told AFP.
"We have earned some respect. You could see that we had fun playing football out there."
The Germans have reached at least the quarterfinal of each of the last seven World Cups and appear destined for another successful tournament after a scintillating display.
After Richard Garcia had given Germany an early scare, Joachim Low's side almost went ahead when Klose was sent racing through on goal, but he fired his shot straight at Australia goalkeeper Mark Schwarzer.
Moments later, Muller found space inside the box and pulled the ball back for Podolski, who fired a first-time shot through the palms of Schwarzer and into the roof of the net.
Garcia and Jason Culina both had half chances for the Australians before Klose almost gave Germany a 2-0 lead.
Playmaker Mesut Ozil, one of the game's outstanding players, fed the ball to Podolski, whose low cross was fired wastefully wide by the unmarked Klose.
But Klose did not have to wait long for his 11th goal in World Cup finals.
Lahm whipped in a fine cross from the right and the Bayern Munich striker darted in ahead of Schwarzer before planting his header into the top corner.
Australia made a bright start to the second period and were denied a penalty when the ball appeared to strike the hand of Germany defender Per Mertesacker.
Moments later Brett Holman worked some space for himself but dragged his left-footed shot wide.
After 55 minutes, Australia were reduced to 10 men when Cahill clattered into Bastian Schweinsteiger and was shown a straight red card by Mexican referee Marco Rodriguez.
That decision effectively ended the game as a contest and it was no surprise when Germany extended their lead, as Muller swivelled inside the area and planted a low shot off the inside of a post.
Brazilian-born substitute Cacau was the next to get on the scoresheet, turning in a low cross from Ozil.
Low's men cruised their way through the rest of the match to record their sixth straight victory in the opening game of a World Cup.
Ghana 1-0 Serbia
Striker Gyan, who plays for French club Rennes, emphatically converted the winner from the spot past Vladimir Stojkovic in the 84th minute to the obvious delight of the partisan crowd.
The victory was the first by an African team at this year's World Cup.
Ghana were awarded their penalty after Serbia substitute Zdravko Kuzmanovic needlessly hand-balled a cross which looked to be drifting harmlessly out of his team's penalty area.
Amid delirious celebrations of the African supporters in the Loftus Versfeld Stadium, Serbia struggled to find an equalizer and it was Ghana, the four-time African champions, who should have made it 2-0 before the final whistle.
Ghana -- popularly known as the Black Stars -- started the match at a high tempo and created chances throughout the match, never allowing the Serbian defense to settle.
This attacking pattern was set early on when Rosenborg midfielder Anthony Annan volleyed the ball wide after two minutes and Ghana's captain John Mensah headed a free kick wide of the far post in the 19th minute.
Ghana continued to press forward in the second half and came closest to scoring when Gyan rose high above the Serbian defense meeting a long throw from John Pantsil, only to head the ball just wide of Stojkovic's left post.
Serbia created fewer chances than their opponents but probably had the better opportunities to score.
The giant Serbia striker Nikola Zigic should have given his country the lead in the 58th minute when he met Dejan Stankovic's cross at the far post but his control let him down and the ball dribbled away to safety.
And later, when Serbia had been reduced to 10 men after Aleksandar Lukovic received his second yellow card in the 73rd minute, Serbia squandered a fantastic opportunity to break the deadlock.
Striker, Danko Lazovic broke away from Fulham's John Pantsil on the left goal-line and managed to cut the ball back into the middle of the area which Milos Krasic then struck fiercely at goalkeeper Richard Kingson, who parried the ball to safety.
The resulting corner saw Manchester United's Nemanja Vidic narrowly head over the crossbar.
Serbia meet Germany next Friday in Port Elizabeth, while Ghana play Australia in Rustenburg on Saturday.